{"id":6867,"date":"2026-09-12T14:42:30","date_gmt":"2026-09-12T09:12:30","guid":{"rendered":"https:\/\/mymockmate.com\/notes\/?p=6867"},"modified":"2026-09-12T15:53:44","modified_gmt":"2026-09-12T10:23:44","slug":"class-9-exercise-6-1-perimeter-of-a-circle","status":"publish","type":"post","link":"https:\/\/mymockmate.com\/notes\/class-9-exercise-6-1-perimeter-of-a-circle\/","title":{"rendered":"Class 9 | Maths | Exercise 6.1 \u2013 Perimeter of a Circle"},"content":{"rendered":"<div class=\"mymoc-top mymoc-entity-placement\" id=\"mymoc-1051283283\"><div id=\"mymoc-407139175\"><a href=\"https:\/\/amzn.to\/4fDWGbw\" aria-label=\"smartwatch\"><img src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/smartwatch.png\" alt=\"\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/smartwatch.png 1717w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/smartwatch-300x71.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/smartwatch-1024x243.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/smartwatch-768x182.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/smartwatch-1536x364.png 1536w\" sizes=\"(max-width: 1717px) 100vw, 1717px\" width=\"1717\" height=\"407\"><\/a><\/div><\/div>\n<h2 class=\"wp-block-heading\">Measuring Space: Perimeter and Area<\/h2>\n\n\n\n<h2 class=\"wp-block-heading\">Introduction<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Perimeter means the <strong>total distance around the boundary of a shape<\/strong>. For a circle, the perimeter is called its <strong>circumference<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In Exercise 6.1, students apply the circumference formula, arc-length formula, properties of sectors and semicircles, and relationships between the perimeter and radius of circles. The textbook instructs us to use <strong>&pi; &asymp; 22\/7 unless stated otherwise<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Key Formulas<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Circumference of a circle:<\/strong><br><strong>C = 2&pi;r = &pi;d<\/strong><\/li>\n\n\n\n<li><strong>Length of an arc:<\/strong><br><strong>Arc length = (&theta;\/360&deg;) &times; 2&pi;r<\/strong><\/li>\n\n\n\n<li><strong>Perimeter of a sector:<\/strong><br><strong>Perimeter = 2r + arc length<\/strong><\/li>\n\n\n\n<li><strong>Semicircle arc:<\/strong><br><strong>&pi;r<\/strong><\/li>\n\n\n\n<li><strong>Quarter-circle arc:<\/strong><br><strong>&pi;r\/2<\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Glossary<\/h1>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Term<\/th><th>Meaning<\/th><\/tr><\/thead><tbody><tr><td><strong>Perimeter<\/strong><\/td><td>Total length around the boundary of a closed shape<\/td><\/tr><tr><td><strong>Circumference<\/strong><\/td><td>Perimeter of a circle<\/td><\/tr><tr><td><strong>Radius (r)<\/strong><\/td><td>Distance from the centre of a circle to its boundary<\/td><\/tr><tr><td><strong>Diameter (d)<\/strong><\/td><td>A line segment passing through the centre and joining two points on a circle<\/td><\/tr><tr><td><strong>Arc<\/strong><\/td><td>A curved part of the circumference of a circle<\/td><\/tr><tr><td><strong>Sector<\/strong><\/td><td>A region bounded by two radii and an arc<\/td><\/tr><tr><td><strong>Central Angle<\/strong><\/td><td>The angle made by an arc at the centre of a circle<\/td><\/tr><tr><td><strong>&pi; (Pi)<\/strong><\/td><td>The ratio of circumference to diameter of a circle; here &pi; is approximated by 22\/7<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">The chapter defines perimeter as the total length around a shape&rsquo;s border and gives the circumference of a circle as <strong>2&pi;r<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Flowchart<\/h1>\n\n\n\n<figure class=\"wp-block-image size-large\"><img fetchpriority=\"high\" decoding=\"async\" width=\"975\" height=\"1024\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/09\/image-975x1024.png\" alt=\"\" class=\"wp-image-6868\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/09\/image-975x1024.png 975w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/09\/image-286x300.png 286w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/09\/image-191x200.png 191w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/09\/image-768x806.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/09\/image.png 1224w\" sizes=\"(max-width: 975px) 100vw, 975px\"><\/figure>\n\n\n\n<h1 class=\"wp-block-heading\">Question<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Question 1<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>The perimeter of a circle is 44 cm. What is its radius?<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">We know:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>C = 2&pi;r<\/strong><\/p>\n\n\n\n<div class=\"internal-linking-related-contents\"><a href=\"https:\/\/mymockmate.com\/notes\/class-9-maths-exercise-1-1-solutions-coordinate-geometry-ncert-solutions\/\" class=\"template-2\"><span class=\"cta\">Related Topic to Read more<\/span><span class=\"postTitle\">NCERT Class 9 Maths Exercise 1.1 Solutions | Coordinate Geometry NCERT Solutions<\/span><\/a><\/div><p class=\"wp-block-paragraph\">Given:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>C = 44 cm<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Using &pi; = 22\/7:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>44 = 2 &times; 22\/7 &times; r<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore,<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>r = 44 &times; 7 \/ 44<\/strong><\/p>\n\n\n\n<div class=\"internal-linking-related-contents\"><a href=\"https:\/\/mymockmate.com\/notes\/class-9-maths-exercise-1-2-solutions-coordinate-geometry-ncert-solutions\/\" class=\"template-2\"><span class=\"cta\">Related Topic to Read more<\/span><span class=\"postTitle\">NCERT Class 9 Maths Exercise 1.2 Solutions | Coordinate Geometry NCERT Solutions<\/span><\/a><\/div><p class=\"wp-block-paragraph\"><strong>r = 7 cm<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>The radius of the circle is 7 cm.<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h2 class=\"wp-block-heading\">Question 2<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Calculate the circumference, correct to <strong>3 significant figures<\/strong>, for circles with the following radii.<\/p><div class=\"mymoc-middle mymoc-entity-placement\" id=\"mymoc-415203159\"><div id=\"mymoc-459858983\"><a href=\"https:\/\/amzn.to\/3S4CntS\" aria-label=\"Stationeries\"><img src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/Stationeries.png\" alt=\"\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/Stationeries.png 1303w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/Stationeries-300x89.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/Stationeries-1024x304.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/Stationeries-768x228.png 768w\" sizes=\"(max-width: 1303px) 100vw, 1303px\" width=\"1080\" height=\"100\"><\/a><\/div><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">(i) Radius = 7 cm<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>C = 2&pi;r<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= 2 &times; 22\/7 &times; 7<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= <strong>44 cm<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer: <strong>44.0 cm<\/strong><\/h3>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h3 class=\"wp-block-heading\">(ii) Radius = 10 cm<\/h3>\n\n\n\n<div class=\"internal-linking-related-contents\"><a href=\"https:\/\/mymockmate.com\/notes\/class-9-maths-end-of-chapter-exercise-solutions-coordinate-geometry-ncert-solutions\/\" class=\"template-2\"><span class=\"cta\">Related Topic to Read more<\/span><span class=\"postTitle\">NCERT Class 9 Maths End of Chapter Exercise Solutions | Coordinate Geometry<\/span><\/a><\/div><p class=\"wp-block-paragraph\">C = 2 &times; 22\/7 &times; 10<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= 440\/7<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= 62.857&hellip;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Correct to 3 significant figures:<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer: <strong>62.9 cm<\/strong><\/h3>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h3 class=\"wp-block-heading\">(iii) Radius = 12 cm<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">C = 2 &times; 22\/7 &times; 12<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= 528\/7<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= 75.428&hellip;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Correct to 3 significant figures:<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer: <strong>75.4 cm<\/strong><\/h3>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answers<\/h3>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Radius<\/th><th>Circumference<\/th><\/tr><\/thead><tbody><tr><td>7 cm<\/td><td><strong>44.0 cm<\/strong><\/td><\/tr><tr><td>10 cm<\/td><td><strong>62.9 cm<\/strong><\/td><\/tr><tr><td>12 cm<\/td><td><strong>75.4 cm<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Question 3<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">Find the length of the arc.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">(i) r = 3.5 cm, &theta; = 60&deg;<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Formula:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Arc length = (&theta;\/360&deg;) &times; 2&pi;r<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Substitute:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= 60\/360 &times; 2 &times; 22\/7 &times; 3.5<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Since 3.5 = 7\/2:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= 1\/6 &times; 22<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= <strong>11\/3 cm<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= <strong>3.67 cm<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer: <strong>3.67 cm<\/strong><\/h3>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h2 class=\"wp-block-heading\">(ii) r = 6.3 m, &theta; = 120&deg;<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Arc length<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= 120\/360 &times; 2 &times; 22\/7 &times; 6.3<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= 1\/3 &times; 39.6<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= <strong>13.2 m<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer: <strong>13.2 m<\/strong><\/h3>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answers<\/h3>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Radius<\/th><th>Central Angle<\/th><th>Arc Length<\/th><\/tr><\/thead><tbody><tr><td>3.5 cm<\/td><td>60&deg;<\/td><td><strong>3.67 cm<\/strong><\/td><\/tr><tr><td>6.3 m<\/td><td>120&deg;<\/td><td><strong>13.2 m<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Question 4<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Find the perimeter of a sector of radius 14 cm and sector angle 75&deg;.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The perimeter contains:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Two radii<\/li>\n\n\n\n<li>One curved arc<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Find the arc length<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Arc length<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= 75\/360 &times; 2 &times; 22\/7 &times; 14<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= 75\/360 &times; 88<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= <strong>55\/3 cm<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= <strong>18.33 cm<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Add the two radii<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Two radii:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= 14 + 14<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= <strong>28 cm<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore,<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Perimeter<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= 28 + 18.33<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= <strong>46.33 cm<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>The perimeter of the sector is approximately 46.3 cm.<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Question 5<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">Find the perimeter of each shape in Fig. 6.14. The exercise specifies that the arcs should be treated as quarter, half or three-quarter circles as appropriate.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">(i)<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The shape has two straight sections of 80 m each and two semicircular ends with diameter 60 m.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Straight portions:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>80 + 80 = 160 m<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The two semicircles together make one complete circle of diameter 60 m.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Circular part:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>&pi; &times; 60 = 60 &times; 22\/7<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= 188.57 m<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore,<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>P = 160 + 188.57<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer: <strong>348.57 m<\/strong><\/h3>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h3 class=\"wp-block-heading\">(ii)<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The outer semicircle has diameter 12 cm and the inner semicircle has diameter 8 cm.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The two straight portions together measure:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>12 &minus; 8 = 4 cm<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The two semicircular arcs together have length equivalent to:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>&pi;(12\/2) + &pi;(8\/2)<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= 6&pi; + 4&pi;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= 10&pi;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore,<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">P = 4 + 10 &times; 22\/7<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= <strong>35.43 cm<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer: <strong>35.43 cm<\/strong><\/h3>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h3 class=\"wp-block-heading\">(iii)<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The boundary consists of four semicircular arcs, each based on a side of length 10 cm.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Four semicircles together:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>4 &times; (&pi; &times; 10\/2)<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= 20&pi;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= 20 &times; 22\/7<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer: <strong>62.86 cm<\/strong><\/h3>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h3 class=\"wp-block-heading\">(iv)<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The boundary consists of three semicircular arcs, each with diameter 12 cm.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">P = 3 &times; (&pi; &times; 12\/2)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= 18&pi;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= 18 &times; 22\/7<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer: <strong>56.57 cm<\/strong><\/h3>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h3 class=\"wp-block-heading\">(v)<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">There are four semicircular arcs, each with diameter 14 cm.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">P = 4 &times; (&pi; &times; 14\/2)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= 28&pi;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= 28 &times; 22\/7<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer: <strong>88 cm<\/strong><\/h3>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h3 class=\"wp-block-heading\">(vi)<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The outer semicircle has diameter 28 cm, while the three smaller semicircular arcs together have the same total diameter, 28 cm.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Thus, the total curved length is equivalent to one complete circle of diameter 28 cm.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">P = &pi; &times; 28<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= 28 &times; 22\/7<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer: <strong>88 cm<\/strong><\/h3>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h3 class=\"wp-block-heading\">(vii)<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The three straight dimensions shown form a <strong>6&ndash;8&ndash;10 triangle<\/strong>. The boundary contains semicircles on all three sides.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Total perimeter:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= &pi;\/2 &times; (6 + 8 + 10)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= &pi;\/2 &times; 24<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= 12&pi;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= 12 &times; 22\/7<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer: <strong>37.71 cm<\/strong><\/h3>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h3 class=\"wp-block-heading\">(viii)<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The large semicircle has diameter:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>4 + 4 + 4 = 12 cm<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The three smaller semicircles each have diameter 4 cm.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Large semicircle:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= &pi; &times; 12\/2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= 6&pi;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Three smaller semicircles:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= 3 &times; &pi; &times; 4\/2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= 6&pi;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Total:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= 12&pi;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= 12 &times; 22\/7<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer: <strong>37.71 cm<\/strong><\/h3>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h3 class=\"wp-block-heading\">(ix)<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The large semicircle has diameter:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>10 + 10 = 20 cm<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The two smaller semicircular arcs each have diameter 10 cm.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Total curved length:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= &pi; &times; 20\/2 + 2 &times; (&pi; &times; 10\/2)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= 10&pi; + 10&pi;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= 20&pi;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= 20 &times; 22\/7<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer: <strong>62.86 cm<\/strong><\/h3>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h2 class=\"wp-block-heading\">Question 5 &ndash; Answer Table<\/h2>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Figure<\/th><th>Perimeter<\/th><\/tr><\/thead><tbody><tr><td>(i)<\/td><td><strong>348.57 m<\/strong><\/td><\/tr><tr><td>(ii)<\/td><td><strong>35.43 cm<\/strong><\/td><\/tr><tr><td>(iii)<\/td><td><strong>62.86 cm<\/strong><\/td><\/tr><tr><td>(iv)<\/td><td><strong>56.57 cm<\/strong><\/td><\/tr><tr><td>(v)<\/td><td><strong>88 cm<\/strong><\/td><\/tr><tr><td>(vi)<\/td><td><strong>88 cm<\/strong><\/td><\/tr><tr><td>(vii)<\/td><td><strong>37.71 cm<\/strong><\/td><\/tr><tr><td>(viii)<\/td><td><strong>37.71 cm<\/strong><\/td><\/tr><tr><td>(ix)<\/td><td><strong>62.86 cm<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">The actual Fig. 6.14 diagrams and their dimensions are shown in the uploaded textbook pages.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Question 6<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>The diameter of a car tyre is 56 cm.<\/strong><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">(i) Distance travelled in one revolution<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">One revolution covers one circumference.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">C = &pi;d<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= 22\/7 &times; 56<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= <strong>176 cm<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>The car travels 176 cm, or 1.76 m, in one revolution.<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h2 class=\"wp-block-heading\">(ii) Revolutions in 10 km<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Convert 10 km into centimetres:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>10 km = 1,000,000 cm<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Number of revolutions:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= Total distance &divide; Distance per revolution<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= 1,000,000 &divide; 176<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= <strong>5681.818&hellip;<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>The tyre makes approximately 5,682 revolutions.<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Question 7<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">Find the total perimeter of all the petals in each flower.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">(i) Flower with a square of side 14 cm<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Each petal is formed by <strong>two quarter-circle arcs<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Radius of each arc:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>14\/2 = 7 cm<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Length of one quarter-circle:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= &pi;r\/2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= 7&pi;\/2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Each petal has two such arcs:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= 7&pi;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">There are four petals:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= 4 &times; 7&pi;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= 28&pi;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= 28 &times; 22\/7<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer: <strong>88 cm<\/strong><\/h3>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h2 class=\"wp-block-heading\">(ii) Flower with a regular hexagon of side 42 cm<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The arcs have radius <strong>42 cm<\/strong> and each petal is bounded by two arcs corresponding to 60&deg;.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Length of one 60&deg; arc:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= 60\/360 &times; 2&pi; &times; 42<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= 14&pi;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Each petal has two arcs:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= 28&pi;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">There are six petals:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= 6 &times; 28&pi;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= 168&pi;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">= 168 &times; 22\/7<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer: <strong>528 cm<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The textbook identifies the centres of the arcs in Fig. 6.15A as the midpoints of the square&rsquo;s sides and in Fig. 6.15B as the vertices of the hexagon.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Question 8<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>The ratio of the perimeters of two circles is 5 : 4. Find the ratio of their radii.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">For any circle:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>C = 2&pi;r<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore, circumference is directly proportional to radius:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>C &prop; r<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">So,<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>C&#8321; : C&#8322; = r&#8321; : r&#8322;<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Given:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>C&#8321; : C&#8322; = 5 : 4<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore,<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer: <strong>The ratio of their radii is 5 : 4.<\/strong><\/h3>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Real Life Example<\/h1>\n\n\n\n<h3 class=\"wp-block-heading\">Running Tracks<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The chapter introduces the idea of perimeter through athletics tracks. Runners in outer lanes start ahead of runners in inner lanes because the curved portions of the outer lanes have larger radii and therefore longer circumferences. The stagger compensates for this additional distance.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Car Tyres<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">A tyre&rsquo;s circumference tells us how far a car travels in one complete revolution. For a tyre with diameter 56 cm:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Distance per revolution = &pi;d = 176 cm<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Thus, knowing the diameter of a tyre allows us to estimate the distance travelled and the number of wheel revolutions.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Mind Map<\/h1>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" width=\"1024\" height=\"683\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/09\/image-1-1024x683.png\" alt=\"\" class=\"wp-image-6869\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/09\/image-1-1024x683.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/09\/image-1-300x200.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/09\/image-1-768x512.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/09\/image-1-250x167.png 250w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/09\/image-1-1200x800.png 1200w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/09\/image-1-450x300.png 450w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/09\/image-1.png 1536w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<h1 class=\"wp-block-heading\">Revision Table<\/h1>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Concept<\/th><th>Formula \/ Rule<\/th><th>Example<\/th><\/tr><\/thead><tbody><tr><td>Circumference<\/td><td><strong>2&pi;r<\/strong><\/td><td>r = 7 cm &rarr; 44 cm<\/td><\/tr><tr><td>Circumference using diameter<\/td><td><strong>&pi;d<\/strong><\/td><td>d = 56 cm &rarr; 176 cm<\/td><\/tr><tr><td>Semicircle arc<\/td><td><strong>&pi;r<\/strong><\/td><td>r = 7 cm &rarr; 22 cm<\/td><\/tr><tr><td>Quarter-circle arc<\/td><td><strong>&pi;r\/2<\/strong><\/td><td>r = 7 cm &rarr; 11 cm<\/td><\/tr><tr><td>Arc of angle &theta;<\/td><td><strong>&theta;\/360 &times; 2&pi;r<\/strong><\/td><td>&theta; = 60&deg;, r = 3.5 cm &rarr; 3.67 cm<\/td><\/tr><tr><td>Sector perimeter<\/td><td><strong>2r + arc<\/strong><\/td><td>r = 14 cm, &theta; = 75&deg; &rarr; 46.3 cm<\/td><\/tr><tr><td>Perimeter ratio of circles<\/td><td><strong>C&#8321; : C&#8322; = r&#8321; : r&#8322;<\/strong><\/td><td>5:4 &rarr; radii 5:4<\/td><\/tr><tr><td>Wheel distance<\/td><td><strong>Circumference &times; revolutions<\/strong><\/td><td>1 revolution of d = 56 cm &rarr; 176 cm<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n<div class=\"mymoc-bottom mymoc-entity-placement\" id=\"mymoc-2116944191\"><div id=\"mymoc-4276249593\"><a href=\"https:\/\/amzn.to\/4ehRB6n\" aria-label=\"printers\"><img src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/printers.png\" alt=\"\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/printers.png 1303w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/printers-300x73.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/printers-1024x250.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/printers-768x187.png 768w\" sizes=\"(max-width: 1303px) 100vw, 1303px\" width=\"1303\" height=\"318\"><\/a><\/div><\/div>","protected":false},"excerpt":{"rendered":"<p>Measuring Space: Perimeter and Area Introduction Perimeter means the total distance around the boundary of a shape. For a circle, the perimeter is called its&#8230;<\/p>\n","protected":false},"author":1,"featured_media":6874,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"postBodyCss":"","postBodyMargin":[],"postBodyPadding":[],"postBodyBackground":{"backgroundType":"classic","gradient":""},"footnotes":""},"categories":[4,11],"tags":[],"class_list":["post-6867","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-class-9","category-maths-class-9"],"featured_image_src":"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/09\/Class-9-Exercise-6.1-\u2013-Perimeter-of-a-Circle-1.png","author_info":{"display_name":"Team Mymockmate","author_link":"https:\/\/mymockmate.com\/notes\/author\/bsm_adm\/"},"_links":{"self":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/6867","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/comments?post=6867"}],"version-history":[{"count":5,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/6867\/revisions"}],"predecessor-version":[{"id":6880,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/6867\/revisions\/6880"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/media\/6874"}],"wp:attachment":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/media?parent=6867"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/categories?post=6867"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/tags?post=6867"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}