Question

a cube has a lateral surface area of 2400 sq m. find the surface area of cub

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Answer 1

Given :

Lateral surface area of cube = 2400 sq.m

To Find :

The surface area of cube

Solution :

Lateral surface area of cube is givem by ,

$\\ \star \: {\boxed{\red{\sf{LSA_{(cube)} = 4 {s}^{2} }}}}$

Here ,

s is side of the cube

We have ,

LSA = 2400 sq.m

Substituting the value we have in the formula ,

$\\ : \implies \sf \:2400 \: {m}^{2} = 4 {s}^{2}$

$\\ : \implies \sf \: \frac{2400 \: {m}^{2} }{4} = {s}^{2}$

$\\ : \implies \sf \: 600 \: {m}^{2} = {s}^{2}$

$\\ : \implies \sf \: s = \sqrt{600 \: {m}^{2} }$

$\\ : \implies{\underline{\boxed{\purple{\mathfrak{s = 10 \sqrt{6} \: m}}}}}$

Now , Formula for surface area of cube is ,

$\\ \star \: {\boxed{\red{\sf{TSA_{(cube)} = 6 {s}^{2} }}}}$

Here ,

a is side

Now ,

$\\ : \implies \sf \:TSA_{(cube)} = 6 {(10 \sqrt{6} \: m) }^{2}$

$\\ : \implies \sf \:TSA_{(cube)} = 6(600\: {m}^{2} )$

$\\ : \implies {\underline{\boxed{\pink{\sf{TSA_{(cube)} =3600 \: {m}^{2} }}}}} \: \bigstar$

Hence ,

The surface area of the cube whose lateral surface area is 2400 sq.m is 3600 sq.m

Answer 2

Step-by-step explanation:

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