[et_pb_section fb_built=”1″ admin_label=”Section” module_class=”mainsec” _builder_version=”4.10.4″ _module_preset=”default” background_color=”#e0f2fd” z_index=”1″ custom_padding=”5px||5px||true|false” locked=”off” collapsed=”off” global_colors_info=”{}”][et_pb_row column_structure=”3_5,2_5″ custom_padding_last_edited=”on|phone” _builder_version=”4.10.8″ _module_preset=”default” background_color=”#FFFFFF” width=”100%” max_width=”1310px” custom_padding=”|51px|40px|51px|false|true” custom_padding_tablet=”” custom_padding_phone=”|40px|30px|40px|false|true” border_radii=”on|10px|10px|10px|10px” global_colors_info=”{}”][et_pb_column type=”3_5″ admin_label=”Column L” _builder_version=”4.9.10″ _module_preset=”default” global_colors_info=”{}”][et_pb_text admin_label=”Acute Angles
\n” _builder_version=”4.11.3″ _module_preset=”default” header_font=”|700|||||||” header_text_align=”left” header_font_size=”50px” header_line_height=”1.18em” custom_padding=”|0px||4px|false|false” header_font_size_tablet=”” header_font_size_phone=”35px” header_font_size_last_edited=”on|phone” global_colors_info=”{}”]<\/p>\n
[\/et_pb_text][et_pb_text admin_label=”Text” _builder_version=”4.13.1″ _module_preset=”default” text_font_size=”16px” header_2_font=”|600|||||||” header_2_text_color=”#a01414″ header_3_font=”|600|||||||” custom_padding=”15px|15px|1px|4px|false|false” global_colors_info=”{}”]<\/p>\n
<\/span><\/p>\n A three-dimensional solid figure in which all its faces are of equal dimension and the length of its edges are all equal, i.e., all its faces are squares is called a <\/span>cube<\/b>. The area of a cube is the area that is enclosed by all the faces of the cube and it is<\/span> calculated using the formula:<\/span><\/p>\n \u00a0Area of Cube = 6 \\times a^{2} <\/span><\/span>, where a is the length of the side of the cube.<\/span><\/p>\n <\/p>\n The surface area of a cube can be of two types that are:<\/span><\/p>\n <\/span><\/p>\n The total surface of a cube is the area enclosed by all the six faces in the cube.<\/span><\/p>\n [\/et_pb_text][et_pb_image src=”https:\/\/eistudymaterial.s3.amazonaws.com\/tsf-cube.png” title_text=”tsf cube” align=”center” _builder_version=”4.13.1″ _module_preset=”default” min_height=”226px” custom_margin=”-35px||||false|false” global_colors_info=”{}”][\/et_pb_image][et_pb_text _builder_version=”4.11.3″ _module_preset=”default” custom_margin=”||-66px|||” custom_padding=”||56px|||” global_colors_info=”{}”]<\/p>\n A Cube<\/i><\/b><\/p>\n For a cube with length \u2018a\u2019 the total surface area is actually the total area enclosed by the figure below:<\/span><\/p>\n <\/span><\/p>\n [\/et_pb_text][et_pb_image src=”https:\/\/eistudymaterial.s3.amazonaws.com\/tsf-2.png” title_text=”tsf 2″ align=”center” _builder_version=”4.11.3″ _module_preset=”default” min_height=”244px” global_colors_info=”{}”][\/et_pb_image][et_pb_text _builder_version=”4.11.3″ _module_preset=”default” header_2_text_color=”#a01414″ custom_margin=”-35px||-66px||false|false” custom_padding=”||56px|||” global_colors_info=”{}”]<\/p>\n Total Surface Area of a Cube<\/i><\/b><\/b><\/p>\n Here the length of the side of each square is \u2018a\u2019 and there are 6 such squares.\u00a0<\/span><\/p>\n We know that area of a square = <\/span>(length of side)^{2}<\/span><\/span>,<\/span><\/p>\n Hence the formula for the Total Surface Area is:<\/span><\/p>\n <\/span><\/p>\n <\/strong><\/p>\n The unit of measurement of the area is \u2018square units\u2019. For example \\mathrm{cm}^{2}, \\mathrm{~m}^{2}, \\text { etc. }<\/span><\/span><\/strong><\/p>\n <\/span><\/strong><\/p>\n The lateral surface includes only the sides of the cube, i.e., it excludes the top and bottom of the cube. Hence, while calculating the lateral surface area, areas of the top and bottom faces are excluded.<\/span><\/p>\n For a cube with length \u2018a\u2019 the lateral surface area of the cube is the total area enclosed by the figure below:<\/span><\/p>\n [\/et_pb_text][et_pb_image src=”https:\/\/eistudymaterial.s3.amazonaws.com\/LSf.png” title_text=”LSf” align=”center” _builder_version=”4.11.3″ _module_preset=”default” custom_margin=”18px||||false|false” global_colors_info=”{}”][\/et_pb_image][et_pb_text _builder_version=”4.13.1″ _module_preset=”default” header_2_text_color=”#a01414″ custom_margin=”-35px||-66px||false|false” custom_padding=”||56px|||” global_colors_info=”{}”]<\/p>\n Lateral Surface Area of a Cube<\/i><\/b><\/p>\n Here the length of the side of each square is \u2018a\u2019 and there are 4 such squares.\u00a0<\/span><\/p>\n Hence the formula which gives the Lateral Surface Area of a cube is:<\/span><\/p>\n <\/strong><\/p>\n <\/strong><\/p>\n <\/strong><\/p>\n Example 1:<\/strong>\u00a0<\/strong>The length of the side of the cube\u00a0is 20 cm.\u00a0Find the total and lateral surface areas of the cube.<\/span><\/span><\/strong><\/p>\n <\/span><\/p>\n Solution:<\/strong><\/p>\n Given, length of the\u00a0side of the cube, l\u00a0= 20 cm<\/span><\/p>\n \u2234<\/span> The Total Surface area<\/span><\/p>\n =6 l^{2}<\/span><\/span><\/p>\n =\\left(6 \\times 20^{2}\\right) \\mathrm{cm}^{2}=2400 \\mathrm{~cm}^{2}<\/span><\/span><\/p>\n And lateral surface area<\/span><\/p>\n =4 l^{2}<\/span><\/span><\/p>\n =\\left(4 \\times 20^{2}\\right) \\mathrm{cm}^{2}=1600 \\mathrm{~cm}^{2}<\/span><\/span><\/p>\n Hence, the Total Surface Area is 2400 {cm}^{2} <\/span> and Lateral Surface Area is 1600 {cm}^{2} <\/span>.<\/span><\/p>\n <\/span><\/p>\n Example 2<\/span>:<\/b> The total surface area of a cube is 60m^{2}<\/span>. What is the length of each edge of such a cube?<\/span><\/p>\n Solution:<\/b><\/span><\/p>\n Let the length of the cube be x m<\/span><\/p>\n We know the Total Surface area =6 x^{2}=60 \\mathrm{~m}^{2}<\/span><\/span><\/p>\n \\therefore x^{2}=\\frac{60}{6} m^{2}=10 m^{2}<\/span><\/span><\/p>\n \\Rightarrow x=\\sqrt{10} \\mathrm{~m}<\/span><\/span><\/p>\n Therefore, the length of each side of the cube is \\sqrt{10} \\mathrm{~m}<\/span>.<\/span><\/p>\n [\/et_pb_text][\/et_pb_column][et_pb_column type=”2_5″ module_id=”stickysideR” admin_label=”Column R” _builder_version=”4.10.4″ _module_preset=”default” background_color=”#fdefe0″ custom_padding=”25px|25px|25px|25px|true|true” sticky_position=”top” sticky_offset_top=”-280px” sticky_limit_top=”row” sticky_limit_bottom=”row” sticky_position_tablet=”none” sticky_position_phone=”none” sticky_position_last_edited=”on|desktop” sticky_limit_bottom_tablet=”” sticky_limit_bottom_phone=”” sticky_limit_bottom_last_edited=”on|phone” border_radii=”on|15px|15px|15px|15px” box_shadow_style=”preset3″ global_colors_info=”{}”][et_pb_image src=”https:\/\/eistudymaterial.s3.amazonaws.com\/1080×1080.png” alt=”Free Trial banner” title_text=”Mindspark Free Trial Banner” url=”https:\/\/mindspark.in\/free-trial” align=”center” module_class=”adsimg” _builder_version=”4.11.1″ _module_preset=”default” custom_padding=”||||false|false” border_radii=”on|10px|10px|10px|10px” global_colors_info=”{}” transform_styles__hover_enabled=”on|hover” transform_scale__hover_enabled=”on|hover” transform_translate__hover_enabled=”on|desktop” transform_rotate__hover_enabled=”on|desktop” transform_skew__hover_enabled=”on|desktop” transform_origin__hover_enabled=”on|desktop” transform_scale__hover=”102%|102%”][\/et_pb_image][et_pb_text admin_label=”Explore Other Topics [\/et_pb_text][et_pb_text _builder_version=”4.10.7″ _module_preset=”default” text_line_height=”2.2em” link_font_size=”16px” custom_margin=”||0px||false|false” custom_padding=”10px|15px|10px|28px|true|false” locked=”off” global_colors_info=”{}”]<\/p>\n [\/et_pb_text][et_pb_text admin_label=”Related Concepts [\/et_pb_text][et_pb_text _builder_version=”4.13.1″ _module_preset=”default” text_line_height=”2.2em” link_font_size=”16px” custom_margin=”||0px||false|false” custom_padding=”10px|15px|10px|28px|true|false” locked=”off” global_colors_info=”{}”]<\/p>\nThe Surface Area of\u00a0 Cube<\/b><\/h2>\n
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Total Surface Area<\/b><\/h2>\n
Total Surface area of cube =6 \\times a^{2}=6 a^{2}<\/span><\/strong><\/h2>\n
\u00a0\u00a0<\/b>
<\/b>Lateral Surface Area<\/b><\/h2>\nLateral Surface Area =4 \\times a^{2}=4 a^{2}<\/span><\/strong><\/h2>\n
Examples<\/b><\/strong><\/h2>\n
\n” _builder_version=”4.9.11″ _module_preset=”default” header_font=”|700|||||||” header_font_size=”25px” text_orientation=”center” custom_margin=”0px||0px||true|false” custom_padding=”8px|15px|0px|15px|false|true” locked=”off” global_colors_info=”{}”]<\/p>\nExplore Other Topics<\/h1>\n
\n” _builder_version=”4.9.11″ _module_preset=”default” header_font=”|700|||||||” header_font_size=”25px” text_orientation=”center” custom_margin=”0px||0px||true|false” custom_padding=”8px|15px|0px|15px|false|true” locked=”off” global_colors_info=”{}”]<\/p>\nRelated Concepts<\/h1>\n