{"id":4336,"date":"2022-01-26T17:13:45","date_gmt":"2022-01-26T17:13:45","guid":{"rendered":"https:\/\/oryxlearning.com\/company\/?page_id=4336"},"modified":"2022-01-26T17:13:45","modified_gmt":"2022-01-26T17:13:45","slug":"surface-area-of-cones","status":"publish","type":"page","link":"https:\/\/oryxlearning.com\/learn\/surface-area-of-cones\/","title":{"rendered":"Surface Area of Cones"},"content":{"rendered":"[vc_section full_width=”stretch_row” content_placement=”middle” css=”.vc_custom_1633364343825{background-image: url(https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/10-min-scaled.jpg?id=2121) !important;background-position: center !important;background-repeat: no-repeat !important;background-size: cover !important;}” el_id=”bg-sec”][vc_row full_width=”stretch_row_content” el_class=”faaaq”][vc_column width=”1\/12″][\/vc_column][vc_column width=”1\/2″ css=”.vc_custom_1633761494145{border-radius: 1px !important;}”][vc_row_inner content_placement=”middle” el_class=”topheadingg”][vc_column_inner width=”1\/6″][vc_single_image image=”2283″ img_size=”full”][\/vc_column_inner][vc_column_inner width=”5\/6″][vc_column_text]\n<h5>Surface Area of Cones<\/h5>\n[\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=”headingnew”]Concept[\/vc_column_text][vc_column_text]The surface area of a cone is the amount of area occupied by the surface of a cone. A cone is a 3-D shape that has a circular base. This means the base is made up of a radius and diameter. The distance between the center of the base and the topmost part of the cone is the height of the cone. Stacking many triangles and rotating them around an axis gives the shape of a cone. As it has a flat base, thus it has a total surface area as well as a curved surface area.[\/vc_column_text][vc_column_text el_class=”headingnew”]Rules[\/vc_column_text][vc_column_text]<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/surface-area-of-cones\"><img loading=\"lazy\" class=\"alignnone wp-image-5754\" style=\"margin-bottom: 12px;\" src=\"https:\/\/cdn.oryxlearning.com\/media_assets\/1613986416709.svg\" alt=\"\" width=\"211\" height=\"189\" \/><\/a><br \/>\n1. Use the formula <strong>L.A. = \u03c0rl<\/strong> to find the the lateral area of a cone.<br \/>\nUse the formula <strong>S.A. = \u03c0rl + \u03c0r<sup>2<\/sup><\/strong> to find the the <a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/surface-area-of-cones\">surface area of a cone<\/a> where <strong>r<\/strong> is the radius and <strong>l<\/strong> is the slant height of the cone.<br \/>\n2. Substitute the measurements given into the formula.<br \/>\n3. Use order of operations to solve.[\/vc_column_text][vc_column_text el_class=”headingnew”]Example[\/vc_column_text][vc_column_text]<span style=\"color: #16a085;\"><strong>Calculate the surface area of the cone shown below.<br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/surface-area-of-cones\"><img loading=\"lazy\" class=\"alignnone wp-image-5754 \" style=\"margin-top: 13px;\" src=\"https:\/\/cdn.oryxlearning.com\/media_assets\/1606480188998.svg\" alt=\"\" width=\"198\" height=\"220\" \/><\/a><br \/>\n<\/strong><\/span>[\/vc_column_text][vc_column_text el_class=”headingnew”]Solution[\/vc_column_text][vc_column_text]Use the formula <strong>S.A. = \u03c0rl + \u03c0r<sup>2<\/sup><\/strong> to calculate the surface area of a cone.<br \/>\nSubstitute the measurements given into the formula and solve.<br \/>\n<strong>S.A.<\/strong> = \u03c0(6)(6.2) + \u03c0(6)<sup>2<\/sup><\/p>\n<p>Use the order of operations to solve.<br \/>\n<strong>S.A.<\/strong> = 116.867 + 113.097<br \/>\n<strong>S.A.<\/strong> = 229.964 cm<sup>2<\/sup><\/p>\n<p><strong><span style=\"color: red;\">S.A = 230.0 cm<sup>2<\/sup> round to nearest tenth.<\/span><\/strong><br \/>\n[\/vc_column_text][vc_column_text el_class=”headingnew”]Practice Surface Area of Cones[\/vc_column_text][vc_row_inner el_class=”boxxborder”][vc_column_inner][vc_column_text]\n<h5 style=\"margin-bottom: 10px;\">Practice Problem 1<\/h5>\n<p><span style=\"color: #16a085;\"><strong>Calculate the surface area of the cone shown below. <\/strong><\/span><br \/>\nRound to the nearest tenth. Use 3.14 for \u03c0.<br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/surface-area-of-cones\"><img loading=\"lazy\" class=\"alignnone wp-image-4342 size-full\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/5-15.png\" alt=\"\" width=\"216\" height=\"177\" \/><\/a>[\/vc_column_text][vc_single_image image=”2159″ img_size=”full” alignment=”right” onclick=”custom_link” link=”https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/surface-area-of-cones”][\/vc_column_inner][\/vc_row_inner][vc_empty_space][vc_row_inner el_class=”boxxborder”][vc_column_inner][vc_column_text]\n<h5 style=\"margin-bottom: 10px;\">Practice Problem 2<\/h5>\n<p><span style=\"color: #16a085;\"><strong>Calculate the lateral area of the cone shown below.<\/strong><\/span><br \/>\nRound to the nearest tenth. Use 3.14 for \u03c0.<br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/surface-area-of-cones\"><img loading=\"lazy\" class=\"alignnone wp-image-4344 size-full\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/6-7.png\" alt=\"\" width=\"220\" height=\"191\" \/><\/a>[\/vc_column_text][vc_single_image image=”2159″ img_size=”full” alignment=”right” onclick=”custom_link” link=”https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/surface-area-of-cones”][\/vc_column_inner][\/vc_row_inner][vc_empty_space][vc_row_inner el_class=”boxxborder”][vc_column_inner][vc_column_text]\n<h5 style=\"margin-bottom: 10px;\">Practice Problem 3<\/h5>\n<p><span style=\"color: #16a085;\"><strong>Calculate the surface area of the cone shown below. <\/strong><\/span><br \/>\nRound to the nearest tenth. Use 3.14 for \u03c0.<br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/surface-area-of-cones\"><img loading=\"lazy\" class=\"alignnone wp-image-4346 size-full\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/7-6.png\" alt=\"\" width=\"175\" height=\"240\" \/><\/a>[\/vc_column_text][vc_single_image image=”2159″ img_size=”full” alignment=”right” onclick=”custom_link” link=”https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/surface-area-of-cones”][\/vc_column_inner][\/vc_row_inner][vc_empty_space][\/vc_column][vc_column width=”1\/3″ css=”.vc_custom_1633369011398{margin-bottom: 50px !important;}”][vc_row_inner el_class=”stickynotee”][vc_column_inner][vc_single_image image=”2265″ img_size=”full” alignment=”center” css_animation=”fadeIn” css=”.vc_custom_1633509989314{border-radius: 10px !important;}” el_class=”stickypin”][vc_column_text]<strong>Surface area:<\/strong> It is the sum of the areas of all the surfaces of a three-dimensional figure.<\/p>\n<p><strong>Lateral area:<\/strong> It is the surface area of the figure, excluding the area of the base(s) of a three-dimensional figure.<\/p>\n<p><strong>Cone:<\/strong> A three-dimensional figure with one circular base connected by a curved surface to a single vertex.<\/p>\n<p><strong>Slant height<\/strong> \u2013 the height of a lateral face.<\/p>\n<p><strong>Net:<\/strong> A two-dimensional shape that can be modified to form a three-dimensional shape or a solid. A 3-D shape may have different nets.[\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=”boxxborder2″ css=”.vc_custom_1635428071735{border-radius: 10px !important;}”]<span style=\"color: #ed5600;\"><strong>Pre-requisite Skills<\/strong><\/span><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/4th-grade\/nets-of-3-dimensional-figures\"><span style=\"color: #ed5600;\">Nets of 3 Dimensional Figures<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/surface-area-of-prisms\"><span style=\"color: #ed5600;\">Surface Area of Prisms<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/surface-area-of-pyramids\"><span style=\"color: #ed5600;\">Surface Area of Pyramids<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/6th-grade\/surface-area-of-rectangular-prisms\"><span style=\"color: #ed5600;\">Surface Area of Rectangular Prisms<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/surface-area-of-cylinders\"><span style=\"color: #ed5600;\">Surface Area of Cylinders<\/span><\/a>[\/vc_column_text][vc_column_text el_class=”boxxborder2″ css=”.vc_custom_1635428322394{border-top-width: 7px !important;border-right-width: 7px !important;border-bottom-width: 7px !important;border-left-width: 7px !important;background-position: center !important;background-repeat: no-repeat !important;background-size: contain !important;border-left-color: #333399 !important;border-left-style: solid !important;border-right-color: #333399 !important;border-right-style: solid !important;border-top-color: #333399 !important;border-top-style: solid !important;border-bottom-color: #333399 !important;border-bottom-style: solid !important;border-radius: 10px !important;}”]<span style=\"color: #333399;\"><strong>Related Skills<\/strong><\/span><br \/>\n<span style=\"color: #333399;\"><a style=\"color: #333399;\" href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/volume-of-pyramids\">Volume of Pyramids<\/a><\/span><br \/>\n<span style=\"color: #333399;\"><a style=\"color: #333399;\" href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/volume-of-prisms\">Volume of Prisms<\/a><\/span><br \/>\n<span style=\"color: #333399;\"><a style=\"color: #333399;\" href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/volume-of-spheres\">Volume of Spheres<\/a><\/span><br \/>\n<span style=\"color: #333399;\"><a style=\"color: #333399;\" href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/volume-of-cylinders\">Volume of Cylinders<\/a><\/span><br \/>\n<span style=\"color: #333399;\"><a style=\"color: #333399;\" href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/volume-of-cones\">Volume of Cones<\/a><\/span><br \/>\n<span style=\"color: #333399;\"><a style=\"color: #333399;\" href=\"https:\/\/en.oryxlearning.com\/question\/maths\/6th-grade\/volume-of-rectangular-prisms\">Volume of Rectangular Prisms<\/a><\/span>[\/vc_column_text][vc_row_inner equal_height=”yes” el_class=”btninlinespacing”][vc_column_inner][vc_btn title=”Grade 1″ color=”warning” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F1st-grade%2Fmaths|title:Grade%201%20Math||”][vc_btn title=”Grade 2″ color=”danger” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F2nd-grade%2Fmaths|title:Grade%202%20Math||”][vc_btn title=”Grade 3″ color=”violet” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F3rd-grade%2Fmaths|title:Grade%203%20Math||”][vc_btn title=”Grade 4″ color=”blue” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F4th-grade%2Fmaths|title:Grade%204%20Math||”][vc_btn title=”Grade 5″ color=”green” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F5th-grade%2Fmaths|title:Grade%205%20Math||”][vc_btn title=”Grade 6″ color=”info” 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el_class=”btninlinespacing”][vc_column_inner][\/vc_column_inner][\/vc_row_inner][\/vc_column][\/vc_row][\/vc_section]\n","protected":false},"excerpt":{"rendered":"<p>[vc_section full_width=”stretch_row” content_placement=”middle” css=”.vc_custom_1633364343825{background-image: url(https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/10-min-scaled.jpg?id=2121) !important;background-position: center !important;background-repeat: no-repeat !important;background-size: cover !important;}” el_id=”bg-sec”][vc_row full_width=”stretch_row_content” el_class=”faaaq”][vc_column width=”1\/12″][\/vc_column][vc_column width=”1\/2″ css=”.vc_custom_1633761494145{border-radius: 1px !important;}”][vc_row_inner content_placement=”middle” el_class=”topheadingg”][vc_column_inner width=”1\/6″][vc_single_image image=”2283″ img_size=”full”][\/vc_column_inner][vc_column_inner width=”5\/6″][vc_column_text] Surface Area of Cones [\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=”headingnew”]Concept[\/vc_column_text][vc_column_text]The surface area of a cone is the amount of area occupied by the surface of a cone. A cone is a 3-D shape […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v17.0 (Yoast SEO v17.6) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Surface Area of Cones | Oryx Learning<\/title>\n<meta name=\"description\" content=\"The surface area of a cone is the amount of area occupied by the surface of a cone. A cone is a 3-D shape that has a circular base. 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