Question

How do you calculate the total surface area of a cuboid with 12cm length, 4cm width and 7cm height.

Answer 1

Answer:

length = 12cm, width = 4cm , height = 7cm

total surface area = (l*b)+(l*b)+(l*h)+(l*h)+(b*h)+(b*h)

= (12*4)+(12*4)+(12*7)+(12*7)+(4*7)+(4*7)

= 48+48+84+84+28+28

= 320cm

thus, total surface area is 320cm

Answer 2

$\frak{Given}\begin{cases} \sf{ \:\: Length\;of\;cuboid = \frak{12\:cm}}&\\\sf{ \:\: Width\;of\; cuboid=\frak{4\;cm}}&\\\sf{ \:\: Height\;of\; cuboid=\frak{7\;cm}}\end{cases}$

Need to find: The Total Surface Area of Cuboid?

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✇ To Calculate the TSA (Total Surface Area) of a Cuboid, formula is Given by :

$\qquad\star\:\underline{\boxed{\frak{TSA_{\:(Cuboid)} = 2 \bigg(lb + bh + hl\bigg)}}}$

where,

• l is length of cuboid, b is breadth/width of cuboid and h is the height of cuboid.

⠀⠀⠀

$\bf{\dag}\;{\underline{\frak{Substituting\:the\:given\:values,}}}\\\\:\implies\sf TSA_{\:(cuboid)} = 2\bigg(12 \times 4 + 4 \times 7 + 7 \times 12\bigg) \\\\\\:\implies\sf TSA_{\:(cuboid)} = 2\bigg(48 + 28 + 84\bigg)\\\\\\:\implies\sf TSA_{\:(cuboid)} = 2 \times 160\\\\\\:\implies\underline{\boxed{\pmb{\frak{\purple{TSA_{\:(cuboid)} = 320\:cm^2}}}}}\;\bigstar$

$\therefore\:{\underline{\sf{Hence,\; the \;TSA(Total\; Surface\;Area)\:of\: Cuboid\;is\; {\pmb{\sf{320\;cm^2}}}.}}}$⠀

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$\qquad\qquad\boxed{\underline{\underline{\purple{\bigstar \: \bf\:More\:to\:know\:\bigstar}}}}$

• $\sf Volume\:of\:cuboid = l \times b \times h$

• $\sf Curved\:surface\:area\:of\:cuboid = 2(l + b)h$

• $\sf Diagonal\:of\:cuboid = \sqrt{l^2 + b^2 + h^2}$