{"id":4279,"date":"2022-01-26T17:05:24","date_gmt":"2022-01-26T17:05:24","guid":{"rendered":"https:\/\/oryxlearning.com\/company\/?page_id=4279"},"modified":"2022-01-26T17:05:24","modified_gmt":"2022-01-26T17:05:24","slug":"volume-of-cones","status":"publish","type":"page","link":"https:\/\/oryxlearning.com\/learn\/volume-of-cones\/","title":{"rendered":"Volume 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>Volume 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]A cone is a three-dimensional shape that has a circular base and it narrows down to a sharp point called a vertex. The volume of a cone is the space occupied by the cone. The formula to find the volume of a cone, whose radius is ‘<strong>r<\/strong>‘ and height is ‘<strong>h<\/strong>‘ is given as, Volume = <img src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;(\\frac{1}{3})\\pi&space;r^{2}h\" alt=\"\\fn_phv (\\frac{1}{3})\\pi r^{2}h\" align=\"absmiddle\" \/>\u00a0cubic units. Let <strong>A<\/strong> = Area of base of the cone and <strong>h<\/strong> = height of the cone. Therefore, the volume of cone = <img src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;(\\frac{1}{3})\\times&space;A\\times&space;h\" alt=\"\\fn_phv (\\frac{1}{3})\\times A\\times h\" align=\"absmiddle\" \/>). Since the base of the cone is of circular shape, we substitute the area to be <strong>\u03c0r<sup>2<\/sup><\/strong>. Volume of cone = <img src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;(\\frac{1}{3})\\pi&space;\\times&space;r^{2}\\times&space;h\" alt=\"\\fn_phv (\\frac{1}{3})\\pi \\times r^{2}\\times h\" align=\"absmiddle\" \/>\u00a0cubic units. Also, the volume of a cone is one-third of the volume of a cylinder.[\/vc_column_text][vc_column_text el_class=”headingnew”]Rules[\/vc_column_text][vc_column_text]1. Use the formula <img src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;V&space;=&space;\\frac{1}{3}\\pi&space;r^{2}&space;h\" alt=\"\\fn_phv V = \\frac{1}{3}\\pi r^{2} h\" align=\"absmiddle\" \/>\u00a0to find the <a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/volume-of-cones\">volume of the cone.<\/a><br \/>\n2. Substitute in the given values for <strong>r<\/strong> and <strong>h<\/strong>.<br \/>\n3. Solve using order of operations.[\/vc_column_text][vc_column_text el_class=”headingnew”]Example[\/vc_column_text][vc_column_text]<span style=\"color: #16a085;\"><strong>Find the volume of the cone. Round to the nearest tenth.<br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/volume-of-cones\"><img loading=\"lazy\" class=\"alignnone wp-image-4282 \" src=\"https:\/\/cdn.oryxlearning.com\/media_assets\/1606384095028.svg\" alt=\"\" width=\"224\" height=\"229\" \/><\/a><br \/>\n<\/strong><\/span>[\/vc_column_text][vc_column_text el_class=”headingnew”]Solution[\/vc_column_text][vc_column_text]1. Use the formula <strong>V =\u00a0<\/strong> <img src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;\\frac{1}{3}\\pi&space;r^{2}&space;h\" alt=\"\\fn_phv \\frac{1}{3}\\pi r^{2} h\" align=\"absmiddle\" \/>\u00a0to find the volume of the cone.<br \/>\n2. Substitute in the given values for r and h.<br \/>\n<strong>h<\/strong> = 6<br \/>\n<strong>r<\/strong> = 3<br \/>\n3. Solve using order of operations.<br \/>\n<strong>V = <img src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;\\frac{1}{3}\\pi&space;(3)^{2}&space;(6)\" alt=\"\\fn_phv \\frac{1}{3}\\pi (3)^{2} (6)\" align=\"absmiddle\" \/><\/strong><br \/>\n<strong>V = <span style=\"color: red;\">56.5 in<sup>3<\/sup><\/span><\/strong><\/p>\n[\/vc_column_text][vc_column_text el_class=”headingnew”]Practice Volume 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>Find the volume of the cone. Round to the nearest tenth.<\/strong><\/span><br \/>\nUse 3.14 for \u03c0.<br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/volume-of-cones\"><img loading=\"lazy\" class=\"alignnone wp-image-4285 size-full\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/2-39.png\" alt=\"\" width=\"214\" height=\"285\" \/><\/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\/volume-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>Find the volume of the cone. Round to the nearest tenth.<\/strong><\/span><br \/>\nUse 3.14 for \u03c0.<br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/volume-of-cones\"><img loading=\"lazy\" class=\"alignnone wp-image-4287 size-full\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/3-31.png\" alt=\"\" width=\"203\" height=\"282\" \/><\/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\/volume-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>Find the volume of the pictured solid, round to the nearest tenth.<\/strong><\/span><br \/>\nUse 3.14 for \u03c0.<br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/volume-of-cones\"><img loading=\"lazy\" class=\"alignnone wp-image-4289 size-full\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/4-23.png\" alt=\"\" width=\"240\" height=\"289\" \/><\/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\/volume-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>Volume<\/strong>: It is the measure of the space occupied by a solid. Volume is measured in cubic units.<\/p>\n<p><strong>Cone<\/strong>: A three-dimensional figure with one circular base connected by a curved surface to a single vertex.[\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=”boxxborder2″ css=”.vc_custom_1635414868092{border-radius: 10px !important;}”]<span style=\"color: #ed5600;\"><strong>Pre-requisite Skills<\/strong><\/span><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/6th-grade\/volume-of-rectangular-prisms\"><span style=\"color: #ed5600;\">Volume of Rectangular Prisms<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/volume-of-prisms\"><span style=\"color: #ed5600;\">Volume of Prisms<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/volume-of-cylinders\"><span style=\"color: #ed5600;\">Volume of Cylinders<\/span><\/a>[\/vc_column_text][vc_column_text el_class=”boxxborder2″ css=”.vc_custom_1635414911188{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\/surface-area-of-prisms\">Surface Area of Prisms<\/a><\/span><br \/>\n<span style=\"color: #333399;\"><a style=\"color: #333399;\" href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/surface-area-of-pyramids\">Surface Area of Pyramids<\/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\/surface-area-of-cylinders\">Surface Area of Cylinders<\/a><\/span><br \/>\n<span style=\"color: #333399;\"><a style=\"color: #333399;\" href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/surface-area-of-cones\">Surface Area of Cones<\/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” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F6th-grade%2Fmaths|title:Grade%206%20Math||”][vc_btn title=”Grade 7″ color=”vista-blue” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F7th-grade%2Fmaths|title:Grade%207%20Math||”][vc_btn title=”Grade 8″ color=”mulled-wine” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F8th-grade%2Fmaths|title:Grade%208%20Math||”][\/vc_column_inner][\/vc_row_inner][vc_row_inner equal_height=”yes” el_class=”btninlinespacing”][vc_column_inner][vc_btn title=”Graphs” color=”warning” link=”url:https%3A%2F%2Fen.oryxlearning.com%2Ftopics%2Fmaths%2Fgraphs|title:Graphs||”][vc_btn title=”Geometry and Spatial sense” color=”danger” link=”url:https%3A%2F%2Fen.oryxlearning.com%2Ftopics%2Fmaths%2Fgeometry-and-spatial-sense|title:Geometry%20and%20Spatial%20sense||”][\/vc_column_inner][\/vc_row_inner][vc_row_inner equal_height=”yes” 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] Volume of Cones [\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=”headingnew”]Concept[\/vc_column_text][vc_column_text]A cone is a three-dimensional shape that has a circular base and it narrows down to a sharp point called a vertex. The volume of […]<\/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>Volume of Cones | Oryx Learning<\/title>\n<meta name=\"description\" content=\"A cone is a three-dimensional shape that has a circular base and it narrows down to a sharp point called a vertex...\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/oryxlearning.com\/learn\/volume-of-cones\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Volume of Cones\" \/>\n<meta property=\"og:description\" content=\"A cone is a three-dimensional shape that has a 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