The surface area of a solid refers to the area covered by the outer surface of the three-dimensional figure. The surface area is broadly classified into the Total Surface Area (TSA) and Lateral Surface Area (LSA).
When it comes to TSA, it is the entire area covered by the outside surface of the solid, whereas LSA is the area covered by the outer surface of the solid excluding the area of the bases.<\/p>\n
Hemisphere is a solid which is obtained when a sphere is divided into two halves. A hemisphere has two kinds of surface areas that are TSA and LSA. The curved surface area of a hemisphere is half of the curved surface area of a sphere.<\/p>\n
Formula:<\/strong><\/p>\n The total surface area of hemisphere = 3 \\pi r^{2}<\/span> <\/p>\n Calculation:<\/b><\/p>\n For calculating the TSA and LSA, different observations are made concerning the type of surface of the three-dimensional figure. We have two types of surfaces in the hemisphere: a curved surface and a circular surface at the base. While calculating the total\u00a0surface\u00a0area\u00a0of\u00a0a hemisphere, we consider the sum of the area of the curved surface and the flat surface. Whereas, in the case of <\/span>CSA\u00a0of\u00a0a hemisphere, we only consider the curved surface area of the hemisphere.<\/span><\/p>\n In case of a hemisphere with radius \u2018r\u2019, we can now formulate,<\/span><\/p>\n <\/span><\/p>\n <\/span><\/p>\n TSA of hemisphere = area of the curved surface + area of the circular base<\/span><\/p>\n \u21d2 TSA = \\frac{1}{2}<\/span>x curved surface area of sphere + \\pi r^{2}<\/span><\/span><\/p>\n \u21d2 TSA = \\frac{1}{2}<\/span>x 4 \\pi r^{2}<\/span><\/span>+ \\pi r^{2}<\/span><\/span><\/p>\n \u21d2 TSA = 2 \\pi \\mathrm{r}^{2}+\\pi \\mathrm{r}^{2}<\/span><\/span><\/p>\n \\therefore T S A=3 \\pi r^{2}<\/span><\/span><\/p>\n <\/span><\/p>\n CSA of hemisphere = \\frac{1}{2}<\/span> x curved surface area of a sphere<\/span><\/p>\n \\Rightarrow \\mathrm{CSA}=\\frac{1}{2}\\times 4 \\pi \\mathrm{r}^{2}<\/span>\u00a0<\/span><\/p>\n \\therefore \\mathrm{CSA}=2 \\pi r^{2}<\/span><\/span><\/p>\n <\/span><\/p>\n <\/span><\/p>\n <\/b><\/p>\n Q1) Calculate the <\/b>curved surface area of a hemisphere with a radius of 7cm?<\/b><\/p>\n A:\u00a0<\/strong> Curved surface area of hemisphere with radius 7 \\mathrm{~cm}=2 \\times \\pi \\times(7)^{2}=308 \\mathrm{~cm}^{2}<\/span><\/span><\/p>\n <\/span><\/p>\n Q2) <\/b>Calculate the <\/b>total surface area of a hemisphere with a radius of 14cm?<\/b><\/p>\n A:<\/strong> Total surface area of a hemisphere with radius 14 \\mathrm{~cm}=3 \\times \\pi \\times(14)^{2}=1848 \\mathrm{~cm}^{2}<\/span>.<\/span><\/p>\n <\/span><\/p>\n Q3) What is the radius of a hemisphere with <\/b>TSA<\/b> 462 \\mathrm{~cm}^{2}<\/span><\/b>?\u00a0<\/b><\/p>\n A: <\/strong>TSA<\/span> of hemisphere =3 \\pi r^{2}<\/span><\/span><\/p>\n\\Rightarrow 462 \\mathrm{~cm}^{2}=3 \\pi r^{2}<\/span>\n\\Rightarrow \\mathrm{r}^{2}=49 \\mathrm{~cm}^{2}<\/span>\n \\Rightarrow \\mathrm{r}=\\sqrt{49}=7\\mathrm{~cm}<\/span><\/span><\/p>\n <\/span><\/p>\n <\/span><\/p>\n <\/b><\/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>\n
The curved surface area of hemisphere = 2 \\pi r^{2}<\/span><\/p>\n![\"\"](\"https:\/\/eistudymaterial.s3.amazonaws.com\/hemp-6.png\")
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