Question

The total surface area of a cube is 937.5 cm.it volume will be

Answer 1

Given:

Total Surface area of cube = 937.5 cm²

To find:

Volume = ?

Formulas used:

1. Total Surface area of cube (TSA) = 6a²
2. Volume of cube = a³

Method:

Let side of cube be 'a' cm

TSA = 937.5 cm²

⇒ 6a² = 937.5 cm²

$\implies \sf{ {a}^{2} = \frac{937.5}{6} }$

$\tt{ \implies \: a {}^{2} = 156.25 }$

$\sf{ \implies \: a = \sqrt{156.25} }$

$\bf{ \implies \: a =12.5 \: cm }$

∴ Side of cube = 12.5 cm

Volume = a³

⇒ Volume = (12.5)³

⇒ Volume = 1953.125 cm³

$\boxed{volume \: of \: cube = 1953.125 \: {cm}^{3} }$