{"id":6950,"date":"2021-12-28T09:15:06","date_gmt":"2021-12-28T09:15:06","guid":{"rendered":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/?page_id=6950"},"modified":"2022-01-03T07:04:12","modified_gmt":"2022-01-03T07:04:12","slug":"volume-of-pyramid-with-examples-and-faqs","status":"publish","type":"page","link":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/math-concepts\/volume-of-pyramid-with-examples-and-faqs\/","title":{"rendered":"Volume of Pyramid with Examples and FAQs"},"content":{"rendered":"<p>[et_pb_section fb_built=&#8221;1&#8243; admin_label=&#8221;Section&#8221; module_class=&#8221;mainsec&#8221; _builder_version=&#8221;4.10.4&#8243; _module_preset=&#8221;default&#8221; background_color=&#8221;#e0f2fd&#8221; z_index=&#8221;1&#8243; custom_padding=&#8221;5px||5px||true|false&#8221; locked=&#8221;off&#8221; collapsed=&#8221;off&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_row column_structure=&#8221;3_5,2_5&#8243; custom_padding_last_edited=&#8221;on|phone&#8221; _builder_version=&#8221;4.10.8&#8243; _module_preset=&#8221;default&#8221; background_color=&#8221;#FFFFFF&#8221; width=&#8221;100%&#8221; max_width=&#8221;1310px&#8221; custom_padding=&#8221;|51px|40px|51px|false|true&#8221; custom_padding_tablet=&#8221;&#8221; custom_padding_phone=&#8221;|40px|30px|40px|false|true&#8221; border_radii=&#8221;on|10px|10px|10px|10px&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_column type=&#8221;3_5&#8243; admin_label=&#8221;Column L&#8221; _builder_version=&#8221;4.9.10&#8243; _module_preset=&#8221;default&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_text admin_label=&#8221;Acute Angles<br \/>\n&#8221; _builder_version=&#8221;4.11.3&#8243; _module_preset=&#8221;default&#8221; header_font=&#8221;|700|||||||&#8221; header_text_align=&#8221;left&#8221; header_font_size=&#8221;50px&#8221; header_line_height=&#8221;1.18em&#8221; custom_padding=&#8221;|0px||4px|false|false&#8221; header_font_size_tablet=&#8221;&#8221; header_font_size_phone=&#8221;35px&#8221; header_font_size_last_edited=&#8221;on|phone&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<h1>Volume of Pyramid with Examples and FAQs<\/h1>\n<p>[\/et_pb_text][et_pb_text admin_label=&#8221;Text&#8221; _builder_version=&#8221;4.13.1&#8243; _module_preset=&#8221;default&#8221; text_font_size=&#8221;16px&#8221; header_2_font=&#8221;|600|||||||&#8221; header_2_text_color=&#8221;#a01414&#8243; header_3_font=&#8221;|600|||||||&#8221; custom_padding=&#8221;15px|15px|54px|4px|false|false&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<h2><b>Volume of pyramid<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">The volume of a pyramid is the total space enclosed by the pyramid. A pyramid is a polyhedron. In a pyramid, the base is a polygon which can be a triangle or square or pentagon, etc., and the lateral sides are triangles that meet at an apex.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Pyramids differ only due to their base. If the base is a triangle it is a triangular pyramid, if it\u2019s a square it\u2019s a square pyramid, if the base is a rectangle then it\u2019s a rectangular pyramid and so on.<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><\/span><\/p>\n<h2><b>The formula for Volume of Pyramid<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">The general formula of volume of a pyramid whose base area is \u2018A\u2019 and the height(altitude) of the pyramid is \u2018h\u2019 can be written as:<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\text { Volume of Pyramid }=\\frac{1}{3} \\times \\mathrm{A} \\times \\mathrm{h}<\/span><\/span><\/p>\n<p>&nbsp;<\/p>\n<h2><b>The formula for different types of Pyramids<\/b><\/h2>\n<p><b><\/b><\/p>\n<p style=\"text-align: center;\"><b><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/eistudymaterial.s3.amazonaws.com\/VOLUME-OF-A-PYRAMID-01-171x300.png\" width=\"400\" height=\"702\" alt=\"\" class=\"wp-image-6952 alignnone size-medium\" srcset=\"https:\/\/eistudymaterial.s3.amazonaws.com\/VOLUME-OF-A-PYRAMID-01-171x300.png 171w, https:\/\/eistudymaterial.s3.amazonaws.com\/VOLUME-OF-A-PYRAMID-01-480x841.png 480w, https:\/\/eistudymaterial.s3.amazonaws.com\/VOLUME-OF-A-PYRAMID-01.png 688w\" sizes=\"(max-width: 400px) 100vw, 400px\" \/><\/b><\/p>\n<h2><b><\/b><\/h2>\n<h2><b>Examples<\/b><\/h2>\n<p><strong>Example 1<\/strong><span style=\"font-weight: 400;\"><strong>:<\/strong> Find the volume of a square pyramid if the base side is 10 cm in length and the height of the pyramid is 15 cm.\u00a0<\/span><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><span style=\"font-weight: 400;\">Given length of the side of a square is 10 cm and the height of the pyramid is 15 cm.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">We know, Volume of a square pyramid <span class=\"katex-eq\" data-katex-display=\"false\">=\\frac{1}{3} a^{2} h<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">where &#8216;a&#8217; is the length of the side of the square and &#8216;h&#8217; is the height of the pyramid <\/span><\/p>\n<p><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\therefore \\text { Volume of the given square pyramid }<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">= <span class=\"katex-eq\" data-katex-display=\"false\">\\frac{1}{3} \\times 10^{2} \\times 15 \\mathrm{~cm}^{3}<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">= <span class=\"katex-eq\" data-katex-display=\"false\">100 \\times 5 \\mathrm{~cm}^{3}=500 \\mathrm{~cm}^{3}<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">Hence the volume of the given pyramid is 500 <span class=\"katex-eq\" data-katex-display=\"false\">{~cm}^{3}<\/span><\/span><span style=\"font-weight: 400;\">.<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><\/span><\/p>\n<p><strong>Example 2<\/strong><span style=\"font-weight: 400;\"><strong>:<\/strong> A pyramid has a triangle of side length 4 cm and altitude 6 cm as its base and the height of the pyramid is 9 cm. Calculate the volume of the triangular pyramid.<\/span><\/p>\n<p><strong>Solution:\u00a0<\/strong><\/p>\n<p><span style=\"font-weight: 400;\">Given that the base triangle has a side length of 4 cm and an altitude of 6 cm.<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\therefore \\text { Area of Triangle }=\\frac{1}{2} \\times 4 \\times 6=12 \\mathrm{~cm}^{2}<\/span><\/span><\/p>\n<span class=\"katex-eq\" data-katex-display=\"false\">\\text { Hence volume of triangular pyramid }<\/span>\n<p>= <span class=\"katex-eq\" data-katex-display=\"false\">\\frac{1}{3} \\times \\mathrm{A} \\times \\mathrm{h}<\/span><\/p>\n<p>= <span class=\"katex-eq\" data-katex-display=\"false\">\\frac{1}{3} \\times 12 \\times 9 \\mathrm{~cm}^{3}=36 \\mathrm{~cm}^{3}<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Therefore, the volume of the pyramid is <span class=\"katex-eq\" data-katex-display=\"false\">36 \\mathrm{~cm}^{3}<\/span>.<\/span><span style=\"font-weight: 400;\"><\/span><\/p>\n<p>[\/et_pb_text][\/et_pb_column][et_pb_column type=&#8221;2_5&#8243; module_id=&#8221;stickysideR&#8221; admin_label=&#8221;Column R&#8221; _builder_version=&#8221;4.10.4&#8243; _module_preset=&#8221;default&#8221; background_color=&#8221;#fdefe0&#8243; custom_padding=&#8221;25px|25px|25px|25px|true|true&#8221; sticky_position=&#8221;top&#8221; sticky_offset_top=&#8221;-280px&#8221; sticky_limit_top=&#8221;row&#8221; sticky_limit_bottom=&#8221;row&#8221; sticky_position_tablet=&#8221;none&#8221; sticky_position_phone=&#8221;none&#8221; sticky_position_last_edited=&#8221;on|desktop&#8221; sticky_limit_bottom_tablet=&#8221;&#8221; sticky_limit_bottom_phone=&#8221;&#8221; sticky_limit_bottom_last_edited=&#8221;on|phone&#8221; border_radii=&#8221;on|15px|15px|15px|15px&#8221; box_shadow_style=&#8221;preset3&#8243; global_colors_info=&#8221;{}&#8221;][et_pb_image src=&#8221;https:\/\/eistudymaterial.s3.amazonaws.com\/1080&#215;1080.png&#8221; alt=&#8221;Free Trial banner&#8221; title_text=&#8221;Mindspark Free Trial Banner&#8221; url=&#8221;https:\/\/mindspark.in\/free-trial&#8221; align=&#8221;center&#8221; module_class=&#8221;adsimg&#8221; _builder_version=&#8221;4.11.1&#8243; _module_preset=&#8221;default&#8221; custom_padding=&#8221;||||false|false&#8221; border_radii=&#8221;on|10px|10px|10px|10px&#8221; global_colors_info=&#8221;{}&#8221; transform_styles__hover_enabled=&#8221;on|hover&#8221; transform_scale__hover_enabled=&#8221;on|hover&#8221; transform_translate__hover_enabled=&#8221;on|desktop&#8221; transform_rotate__hover_enabled=&#8221;on|desktop&#8221; transform_skew__hover_enabled=&#8221;on|desktop&#8221; transform_origin__hover_enabled=&#8221;on|desktop&#8221; transform_scale__hover=&#8221;102%|102%&#8221;][\/et_pb_image][et_pb_text admin_label=&#8221;Explore Other Topics<br \/>\n&#8221; _builder_version=&#8221;4.9.11&#8243; _module_preset=&#8221;default&#8221; header_font=&#8221;|700|||||||&#8221; header_font_size=&#8221;25px&#8221; text_orientation=&#8221;center&#8221; custom_margin=&#8221;0px||0px||true|false&#8221; custom_padding=&#8221;8px|15px|0px|15px|false|true&#8221; locked=&#8221;off&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<h1>Explore Other Topics<\/h1>\n<p>[\/et_pb_text][et_pb_text _builder_version=&#8221;4.10.7&#8243; _module_preset=&#8221;default&#8221; text_line_height=&#8221;2.2em&#8221; link_font_size=&#8221;16px&#8221; custom_margin=&#8221;||0px||false|false&#8221; custom_padding=&#8221;10px|15px|10px|28px|true|false&#8221; locked=&#8221;off&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<div>\n<div class=\"trr\"><a href=\"https:\/\/stgwebsite.mindspark.in\/wordpress\/math-concepts\/#geometry\" class=\"otherc\">Geometry<\/a><\/div>\n<div class=\"trr\"><a href=\"https:\/\/stgwebsite.mindspark.in\/wordpress\/math-concepts\/#trigonometry\" class=\"otherc\">Trigonometry<\/a><\/div>\n<div class=\"trr\"><a href=\"https:\/\/stgwebsite.mindspark.in\/wordpress\/math-concepts\/#operations\" class=\"otherc\">Operations<\/a><\/div>\n<div class=\"trr\"><a href=\"https:\/\/stgwebsite.mindspark.in\/wordpress\/math-concepts\/#numbers\" class=\"otherc\">Numbers<\/a><\/div>\n<\/div>\n<p>[\/et_pb_text][et_pb_text admin_label=&#8221;Related Concepts<br \/>\n&#8221; _builder_version=&#8221;4.9.11&#8243; _module_preset=&#8221;default&#8221; header_font=&#8221;|700|||||||&#8221; header_font_size=&#8221;25px&#8221; text_orientation=&#8221;center&#8221; custom_margin=&#8221;0px||0px||true|false&#8221; custom_padding=&#8221;8px|15px|0px|15px|false|true&#8221; locked=&#8221;off&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<h1>Related Concepts<\/h1>\n<p>[\/et_pb_text][et_pb_text _builder_version=&#8221;4.13.1&#8243; _module_preset=&#8221;default&#8221; text_line_height=&#8221;2.2em&#8221; link_font_size=&#8221;16px&#8221; custom_margin=&#8221;||0px||false|false&#8221; custom_padding=&#8221;10px|15px|10px|28px|true|false&#8221; locked=&#8221;off&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<div>\n<div class=\"trr\"><a href=\"https:\/\/mindspark.in\/studymaterial\/math-concepts\/surface-area-and-volume-formulas\/\" class=\"otherc\">Surface Area and Volume Formula<\/a><\/div>\n<div class=\"trr\"><a href=\"https:\/\/mindspark.in\/studymaterial\/math-concepts\/mensuration-formula-2d-and-3d-shapes\/\" class=\"otherc\">Mensuration Formula<\/a><a href=\"#\" class=\"otherc\"><\/a><\/div>\n<\/div>\n<p>[\/et_pb_text][\/et_pb_column][\/et_pb_row][et_pb_row admin_label=&#8221;Row for space&#8221; 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_module_preset=&#8221;default&#8221; background_color=&#8221;#fff7d6&#8243; width=&#8221;100%&#8221; max_width=&#8221;1310px&#8221; height=&#8221;134px&#8221; custom_margin=&#8221;||50px||false|false&#8221; custom_padding=&#8221;12px||12px||true|false&#8221; border_radii=&#8221;on|11px|11px|11px|11px&#8221; locked=&#8221;off&#8221; collapsed=&#8221;off&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_column type=&#8221;4_4&#8243; _builder_version=&#8221;4.9.10&#8243; _module_preset=&#8221;default&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_image src=&#8221;https:\/\/stgwebsite.mindspark.in\/wordpress\/wp-content\/uploads\/2021\/08\/calloutImage.png&#8221; title_text=&#8221;calloutImage&#8221; show_bottom_space=&#8221;off&#8221; admin_label=&#8221;Image&#8221; module_class=&#8221;img1&#8243; _builder_version=&#8221;4.10.8&#8243; _module_preset=&#8221;default&#8221; width=&#8221;25px&#8221; height=&#8221;60px&#8221; custom_padding=&#8221;2px||2px||true|false&#8221; global_colors_info=&#8221;{}&#8221;][\/et_pb_image][et_pb_text module_class=&#8221;ftstyle&#8221; _builder_version=&#8221;4.9.10&#8243; _module_preset=&#8221;default&#8221; text_orientation=&#8221;center&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<div class=\"ffmanage\">\n<div class=\"textmanagestyle\">\n<div class=\"fone\">\n<p>Ready to get started ?<\/p>\n<\/div>\n<div class=\"sone\">\n<p class=\"ffbtn\"><a href=\"https:\/\/mindspark.in\/free-trial\">Start Free Trial<\/a><\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>[\/et_pb_text][et_pb_image src=&#8221;https:\/\/stgwebsite.mindspark.in\/wordpress\/wp-content\/uploads\/2021\/08\/down-circle.png&#8221; title_text=&#8221;down-circle&#8221; show_bottom_space=&#8221;off&#8221; align=&#8221;right&#8221; module_class=&#8221;img2&#8243; _builder_version=&#8221;4.9.10&#8243; _module_preset=&#8221;default&#8221; width=&#8221;44px&#8221; height=&#8221;18px&#8221; custom_padding=&#8221;2px||2px||true|false&#8221; global_colors_info=&#8221;{}&#8221;][\/et_pb_image][\/et_pb_column][\/et_pb_row][et_pb_row admin_label=&#8221;FAQ Row&#8221; _builder_version=&#8221;4.9.11&#8243; _module_preset=&#8221;default&#8221; width=&#8221;100%&#8221; max_width=&#8221;1310px&#8221; custom_padding=&#8221;|40px||40px|false|true&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_column type=&#8221;4_4&#8243; _builder_version=&#8221;4.9.11&#8243; _module_preset=&#8221;default&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_text admin_label=&#8221;FAQ&#8221; module_class=&#8221;faqstyl&#8221; _builder_version=&#8221;4.13.1&#8243; _module_preset=&#8221;default&#8221; text_font_size=&#8221;16px&#8221; header_font=&#8221;|700|||||||&#8221; header_text_align=&#8221;center&#8221; header_line_height=&#8221;2.5em&#8221; background_color=&#8221;#dbedc6&#8243; max_width=&#8221;80%&#8221; module_alignment=&#8221;center&#8221; custom_margin=&#8221;||||false|false&#8221; custom_padding=&#8221;30px|25px|30px|25px|true|true&#8221; border_radii=&#8221;on|10px|10px|10px|10px&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<h1>Frequently Asked Questions<span style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">\u00a0<\/span><\/span><\/h1>\n<ol><\/ol>\n<h3><strong>Q1. What is the Volume of a Pyramid?<\/strong><strong><\/strong><\/h3>\n<p><span style=\"font-weight: 400;\"><strong>Ans: <\/strong>The volume of a pyramid is the total space enclosed by the pyramid.<br \/>The volume of a pyramid whose base area is &#8216;B&#8217; and height is &#8216; h &#8216; is:<\/span><span class=\"katex-eq katex-rendered\" data-katex-display=\"false\"><span class=\"katex\"><span class=\"katex-mathml\"><\/span><\/span><\/span><\/p>\n<p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mtext>\u00a0Volume\u00a0<\/mtext><mo>=<\/mo><mfrac><mn>1<\/mn><mn>3<\/mn><\/mfrac><mrow><mi mathvariant=\"normal\">B<\/mi><mi mathvariant=\"normal\">h<\/mi><\/mrow><\/mrow><annotation encoding=\"application\/x-tex\"><span class=\"katex-eq\" data-katex-display=\"false\">\\text { Volume }=\\frac{1}{3} \\mathrm{Bh}<\/span><\/annotation><\/semantics><\/math>\n<\/p>\n<h3><strong>Q2. How to calculate the volume of a pyramid if slant height is given?<br \/><\/strong><\/h3>\n<p><strong>Ans:\u00a0 <\/strong>If \u2018a\u2019 is the length of the base edge and \u2018h\u2019 is the height of a regular pyramid then the slant height can be calculated using the Pythagoras theorem.<br \/>Let \u2018l\u2019 be the slant height of the pyramid then we have:<\/p>\n<span class=\"katex-eq\" data-katex-display=\"false\">\\mathrm{l}^{2}=\\left(\\frac{\\mathrm{a}}{2}\\right)^{2}+\\mathrm{h}^{2}<\/span>\n<p><span style=\"font-weight: 400;\">Now from this formula, the height can be obtained if the slant height and length of the base edge is given. And then using the formula of volume of the pyramid the volume can be determined.<\/span><strong><\/strong><\/p>\n<p>[\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Meta Description: We can calculate the sum of the terms in a geometric progression using the formula  S = a(1-r^n)\/(1-r) when r < 1 and  S = a(r^n-1)\/(r-1)when r>1<\/p>\n","protected":false},"author":10,"featured_media":0,"parent":714,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","footnotes":""},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.6 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Volume of Pyramid with Examples and FAQs - mydomain<\/title>\n<meta name=\"description\" content=\"Meta Description: We can calculate the sum of the terms in a geometric progression using the formula S = a(1-r^n)\/(1-r) when r &lt; 1 and S = a(r^n-1)\/(r-1)when r&gt;1\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/stgwebsite.mindspark.in\/studymaterial\/math-concepts\/volume-of-pyramid-with-examples-and-faqs\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Volume of Pyramid with Examples and FAQs - 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