{"id":18854,"date":"2018-01-19T11:49:41","date_gmt":"2018-01-19T11:49:41","guid":{"rendered":"https:\/\/cbselibrary.com\/?p=18854"},"modified":"2020-11-26T12:41:53","modified_gmt":"2020-11-26T07:11:53","slug":"math-labs-activity-lateral-surface-area-right-circular-cone-formula","status":"publish","type":"post","link":"https:\/\/cbselibrary.com\/math-labs-activity-lateral-surface-area-right-circular-cone-formula\/","title":{"rendered":"Math Labs with Activity &#8211; Lateral Surface Area of a Right-Circular Cone\u00a0Formula"},"content":{"rendered":"<h2><span style=\"color: #00ccff;\"><strong>Math Labs with Activity &#8211; Lateral Surface Area of a Right-Circular Cone\u00a0Formula<\/strong><\/span><\/h2>\n<p style=\"text-align: center;\"><span style=\"color: #0000ff;\"><strong>OBJECTIVE<\/strong><\/span><\/p>\n<p>To demonstrate a method to derive a formula for finding the lateral surface area of a right-circular cone (Method 1).<\/p>\n<p><span style=\"color: #0000ff;\"><strong>Materials Required<\/strong><\/span><\/p>\n<ol>\n<li>A model of a right-circular cone made of chart paper<\/li>\n<li>A sheet of white paper<\/li>\n<li>A coloured glazed paper<\/li>\n<li>A geometry box<\/li>\n<li>A pair of scissors<\/li>\n<li>A roll of Sellotape<\/li>\n<\/ol>\n<p><span style=\"color: #0000ff;\"><strong>Theory<\/strong><\/span><br \/>\nA right-circular cone is formed by folding a sector of a circular sheet of paper. When such a cone of slant height l and base radius r (as shown in Figure 33.1) is unfolded,<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-95790\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/01\/Math-Labs-with-Activity-Lateral-Surface-Area-of-a-Right-Circular-Cone-Formula-1.png\" alt=\"Math Labs with Activity - Lateral Surface Area of a Right-Circular Cone\u00a0Formula 1\" width=\"133\" height=\"209\" \/><br \/>\nwe get a sector of a circular sheet of radius l formed by an arc of length 2\u03c0r (as shown in Figure 33.2).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-95791\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/01\/Math-Labs-with-Activity-Lateral-Surface-Area-of-a-Right-Circular-Cone-Formula-2.png\" alt=\"Math Labs with Activity - Lateral Surface Area of a Right-Circular Cone\u00a0Formula 2\" width=\"203\" height=\"214\" \/><\/p>\n<p><span style=\"color: #0000ff;\"><strong>Procedure<\/strong> <\/span><br \/>\n<strong>Step 1:<\/strong> Take the model of the right-circular cone. Mark a point P on its circular edge. Mark its vertex as O.<br \/>\nJoin OP and measure it. Let the length of OP be l (see Figure 33.3).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-95792\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/01\/Math-Labs-with-Activity-Lateral-Surface-Area-of-a-Right-Circular-Cone-Formula-3.png\" alt=\"Math Labs with Activity - Lateral Surface Area of a Right-Circular Cone\u00a0Formula 3\" width=\"162\" height=\"230\" \/><br \/>\nThen, the slant height of the cone is l.<br \/>\n<strong>Step 2:<\/strong> Place the cone over the sheet of white paper. Use a pencil and draw along the edge of the circular base of the cone to get a circle on the white paper. Determine the centre of this circle (by applying the method discussed in Activity 21). Mark it X. Take a point Y on the circumference of this circle. Join XY and measure it. Let this be r (see Figure 33.4).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-95793\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/01\/Math-Labs-with-Activity-Lateral-Surface-Area-of-a-Right-Circular-Cone-Formula-4.png\" alt=\"Math Labs with Activity - Lateral Surface Area of a Right-Circular Cone\u00a0Formula 4\" width=\"178\" height=\"186\" \/><br \/>\nThen, the radius of the base of the cone is r.<br \/>\n<strong>Step 3:<\/strong> Mark a point O&#8217; on the coloured glazed paper. Taking O&#8217; as the centre, draw a circle of the radius l. Mark a point P&#8217; on this circle.<br \/>\n<strong>Step 4:<\/strong> Calculate 2\u03c0r taking \u03c0 = 22\/7 and using the value of r measured in Step 2. Tate a thread of length 2\u03c0r. Place its one end at the point P&#8217; and move it along the circumference of the circle. Mark the point Q&#8217; on the circle where the thread has its other end. Cut the sector P&#8217;OQ&#8217; from the glazed &#8211; paper as shown in Figure 33.5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-95794\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/01\/Math-Labs-with-Activity-Lateral-Surface-Area-of-a-Right-Circular-Cone-Formula-5.png\" alt=\"Math Labs with Activity - Lateral Surface Area of a Right-Circular Cone\u00a0Formula 5\" width=\"218\" height=\"262\" \/><br \/>\n<strong>Step 5:<\/strong> Calculate the surface area of the sector drawn on the glazed paper (see Calculations).<br \/>\n<strong>Step 6:<\/strong> Fold the sector cut from the glazed paper so that the line O&#8217;P&#8217; lies exactly over the line O&#8217;Q&#8217;. Join the two ends of the sector by Sellotape. Place this cone over the model cone. What do you observe?<\/p>\n<p><span style=\"color: #0000ff;\"><strong>Observations<\/strong><\/span><br \/>\nWe observe that the cone formed by folding the sector exactly covers the model cone.<br \/>\nTherefore, the curved area of the model cone = area of the sector used to form the cone.<\/p>\n<p><span style=\"color: #0000ff;\"><strong>Calculations<\/strong><\/span><br \/>\nTo find the area of the sector of the circle forming the cone, we proceed as follows.<br \/>\nLength of the arc P&#8217;Q&#8217; = 2\u03c0r.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-95795\" src=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/01\/Math-Labs-with-Activity-Lateral-Surface-Area-of-a-Right-Circular-Cone-Formula-6.png\" alt=\"Math Labs with Activity - Lateral Surface Area of a Right-Circular Cone\u00a0Formula 6\" width=\"619\" height=\"113\" srcset=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/01\/Math-Labs-with-Activity-Lateral-Surface-Area-of-a-Right-Circular-Cone-Formula-6.png 619w, https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/01\/Math-Labs-with-Activity-Lateral-Surface-Area-of-a-Right-Circular-Cone-Formula-6-300x55.png 300w\" sizes=\"(max-width: 619px) 100vw, 619px\" \/><br \/>\n<strong>\u2234<\/strong> curved area of the model cone = \u03c0rl.<\/p>\n<p><span style=\"color: #0000ff;\"><strong>Result<\/strong> <\/span><br \/>\nThe curved surface area of a right-circular cone having slant height l and radius of the base r is given by \u03c0rl.<\/p>\n<p><strong>Remarks:<\/strong><br \/>\nThe total surface area of a right-circular cone can be determined by adding the area of its circular base, \u03c0r\u00b2, to the curved surface area, \u03c0rl.<br \/>\nThus, total surface area of the cone = \u03c0rl + \u03c0r\u00b2 = \u03c0r(l+r).<\/p>\n<p><a class=\"button-red\" title=\"Math Labs for CBSE Class 10\" href=\"https:\/\/cbselibrary.com\/math-labs-for-cbse-class-10\/\">Math Labs with Activity<\/a><a class=\"button-blue\" title=\"NCERT Class 10 Maths Lab Manual\" href=\"https:\/\/www.cbsetuts.com\/ncert-class-10-maths-lab-manual\/\">Math Labs<\/a><a class=\"button-blue\" title=\"CBSE Class 10 Science Practical Skills\" href=\"http:\/\/www.cbsesamplepapers.info\/cbse-class-10-science-practical-skills\">Science Practical Skills<\/a><a class=\"button-blue\" title=\"NCERT Class 10 Science Lab Manual\" href=\"https:\/\/www.cbsetuts.com\/ncert-class-10-science-lab-manual\/\">Science Labs<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Math Labs with Activity &#8211; Lateral Surface Area of a Right-Circular Cone\u00a0Formula OBJECTIVE To demonstrate a method to derive a formula for finding the lateral surface area of a right-circular cone (Method 1). Materials Required A model of a right-circular cone made of chart paper A sheet of white paper A coloured glazed paper A &#8230; <a title=\"Math Labs with Activity &#8211; Lateral Surface Area of a Right-Circular Cone\u00a0Formula\" class=\"read-more\" href=\"https:\/\/cbselibrary.com\/math-labs-activity-lateral-surface-area-right-circular-cone-formula\/\" aria-label=\"More on Math Labs with Activity &#8211; Lateral Surface Area of a Right-Circular Cone\u00a0Formula\">Read more<\/a><\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[6805],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v17.8 (Yoast SEO v18.4.1) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Math Labs with Activity - Lateral Surface Area of a Right-Circular Cone\u00a0Formula - CBSE Library<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/cbselibrary.com\/math-labs-activity-lateral-surface-area-right-circular-cone-formula\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Math Labs with Activity - Lateral Surface Area of a Right-Circular Cone\u00a0Formula\" \/>\n<meta property=\"og:description\" content=\"Math Labs with Activity &#8211; Lateral Surface Area of a Right-Circular Cone\u00a0Formula OBJECTIVE To demonstrate a method to derive a formula for finding the lateral surface area of a right-circular cone (Method 1). 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