{"id":2330,"date":"2021-09-29T08:36:47","date_gmt":"2021-09-29T08:36:47","guid":{"rendered":"http:\/\/stgwebsite.mindspark.in\/wordpress\/?page_id=2330"},"modified":"2021-12-31T11:11:23","modified_gmt":"2021-12-31T11:11:23","slug":"surface-area-of-a-cuboid-derivation-and-examples","status":"publish","type":"page","link":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/math-concepts\/surface-area-of-a-cuboid-derivation-and-examples\/","title":{"rendered":"SURFACE AREA OF A CUBOID \u2013 DERIVATION AND EXAMPLES"},"content":{"rendered":"

[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=”4.10.6″ _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=”4.10.8″ _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

SURFACE AREA OF A CUBOID \u2013 DERIVATION AND EXAMPLES<\/b><\/h1>\n

[\/et_pb_text][et_pb_text admin_label=”Text” _builder_version=”4.11.3″ _module_preset=”default” text_font_size=”16px” header_2_font=”|600|||||||” header_2_text_color=”#a01414″ header_3_font=”|600|||||||” header_3_text_color=”#777777″ custom_padding=”15px|15px||4px|false|false” global_colors_info=”{}”]<\/p>\n

SURFACE AREA OF A CUBOID<\/b><\/h2>\n

What is a cuboid? It is a three-dimensional shape that has six faces and each one of its faces resembles a rectangle. The cuboid has opposite faces equal to each other. <\/span>The total surface area of a cuboid is the sum of the areas of all its faces.\u00a0<\/i><\/b><\/p>\n

A rectangle has length and breadth but <\/span>a cuboid has length (l), breadth (b) and height<\/i><\/b> (h)<\/i><\/b>as shown in the image below.\u00a0<\/span><\/p>\n

\"\"<\/span><\/p>\n

A two-dimensional shape has an area so the area of the rectangle will be length x breadth. A three-dimensional shape has a surface area which is the sum of the area of all the faces of the cuboid. <\/span>The total surface area of a cuboid is 2 {(l x b) + (b x h) + (h x l)} where l is length, b is breadth and h is height.<\/i><\/b><\/p>\n

For Example: What is the total surface area of a cuboid with the following dimensions?<\/span><\/p>\n

\"\"<\/span><\/p>\n

Ans: The length is 30 cm<\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0The breadth is 10 cm<\/span><\/p>\n

And the height is 20 cm so\u00a0<\/span><\/p>\n

Total surface area (TSA) of the cuboid = 2 {(l x b) + (b x h) + (h x l)}<\/span><\/p>\n

TSA of the cuboid = 2 {(30 x 10) + (10 x 20) + (20 x 30)} = 2200 <\/b>cm<\/span>2<\/sup><\/span><\/p>\n

The unit of the surface area is written as <\/i><\/b>unit<\/span>2<\/span>.<\/span> ( based on whatever is the value of the unit which can be cm, m etc.)<\/span><\/p>\n

Now, the top and bottom faces in a cuboid can be labelled as below:<\/span><\/p>\n

\"\"<\/span><\/p>\n

It includes a top and a bottom along with 4 faces. Now, as we saw before, the TSA includes all 6 faces of the cuboid but when we find the lateral surface area (LSA), then we find the area of all the sides excluding the top and the bottom side.\u00a0<\/span><\/p>\n

Lateral Surface area (LSA) of a cuboid is 2h ( l + b) where l is length, b is breadth and h is height.<\/i><\/b><\/p>\n

For example: What is the lateral surface area of the cuboid with length = 30 cm, breadth = 20 cm and height = 15 cm?<\/span><\/p>\n

Ans: The LSA of a cuboid = 2h (l + b)\u00a0<\/span><\/p>\n

= 2 x 15 (30 + 20)<\/span><\/p>\n

= 2 x 750<\/span><\/p>\n

= 1500 <\/span>cm<\/span>2<\/span><\/p>\n

 <\/p>\n

DERIVATION OF THE SURFACE AREA OF A CUBOID<\/b><\/h3>\n

The formulas for the TSA and LSA can be easily derived by understanding that there are 6 faces of a cuboid.\u00a0<\/span><\/p>\n

\"\"<\/span><\/p>\n

Now, The total area is simply the sum of the area of all the sides. We will simply find the area of each side as shown below in the table:<\/span><\/p>\n\n\n\n\n\n\n\n\n\n
SIDE<\/b><\/td>\nFORMULA for AREA<\/b><\/td>\n<\/tr>\n
ABCD<\/b><\/td>\nl x b<\/span><\/td>\n<\/tr>\n
EFGH<\/b><\/td>\nl x b<\/span><\/td>\n<\/tr>\n
ABFE<\/b><\/td>\nb x h<\/span><\/td>\n<\/tr>\n
DCGH<\/b><\/td>\nb x h<\/span><\/td>\n<\/tr>\n
ADHE<\/b><\/td>\nh x l<\/span><\/td>\n<\/tr>\n
BCGF<\/b><\/td>\nh x l<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n

Therefore, when we add all the above areas we get\u00a0<\/span><\/p>\n

(l x b) + (l x b) + (b x h) + (b x h) + (h x l) + (h x l) = <\/span>2 {(l x b) + (b x h) + (h x l)}<\/b><\/p>\n

Similarly, we can derive the formula for LSA. We can subtract the area of the top ( ABCD) and the bottom (EFHG) from the TSA to get the area of the four sides.\u00a0<\/span><\/p>\n

So, LSA is<\/span><\/p>\n

LSA = TSA \u2013 {(l x b) + (l x b)} = 2 {(l x b) + (b x h) + (h x l)} \u2013 2 (l x b)<\/span><\/p>\n

= 2 {(b x h) + (h x l)}<\/span><\/p>\n

= 2h (l + b)<\/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
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Explore Other Topics<\/h1>\n

[\/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

\n
Geometry<\/a><\/div>\n
Trigonometry<\/a><\/div>\n
Operations<\/a><\/div>\n
Numbers<\/a><\/div>\n<\/div>\n

[\/et_pb_text][et_pb_text admin_label=”Related Concepts
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Related Concepts<\/h1>\n

[\/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” hover_enabled=”0″ locked=”off” global_colors_info=”{}” sticky_enabled=”0″]<\/p>\n

\n
Surface Area and Volume Formula<\/a><\/div>\n
CSA of Cuboid<\/a><\/div>\n
Volume of Cuboid<\/a><\/div>\n<\/div>\n

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Frequently Asked Questions<\/h1>\n

1.<\/strong> What is the value of <\/span>\u221a8 up to 4 decimal places?<\/span><\/p>\n

Ans:<\/strong> The value of root 8 up to 4 decimal places is 2.8284<\/span><\/p>\n

2.<\/strong> Is <\/span>\u221a8 an irrational or rational number?<\/span><\/p>\n

Ans:<\/strong> \u221a8 is an irrational number because the value of \u221a8 doesn\u2019t terminate and keeps on extending.<\/span><\/p>\n

3.<\/strong> Express root 8 in exponential form.<\/span><\/p>\n

Ans:<\/strong> The exponential form of root 8 is (8)<\/span>1\/2<\/span><\/p>\n

[\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"

The square root of 64 is 8, and we can calculate this by the prime factorisation method. Let us calculate the value of root 64 to prove it is a rational number. <\/p>\n","protected":false},"author":7,"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":"\nSurface Area of a Cuboid - mydomain<\/title>\n<meta name=\"description\" content=\". 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