Question

The surface area of a cube is 216 sq. cm. What is its volume?​

Answer 1

$\small\bold{\underline{\sf{\purple{Given}}}}$

• Surface area of a Cube = 216sq.cm

$\small\bold{\underline{\sf{\red{To\:Find:-}}}}$

• The Volume of Cube.

$\small\bold{\underline{\sf{\blue{solution:-}}}}$

${\boxed{\rm{\red{Surface\:area\:of\:Cube= 6(side)^2}}}}$

${\boxed{\rm{\green{Volume\:of\:cube = (side)^3}}}}$

Now,

$\implies\rm{Surface\:area\:of\:Cube = 6(side)^2}$

$\implies\rm{216sq.cm = 6(side)^2}$

$\implies\rm{(side)^2 = \dfrac{216}{6}}$

$\implies\rm{(side)^2 = 36}$

$\implies\rm{(side = \sqrt{36}}$

$\implies\rm{Side = 6cm}$

Therefore,

$\implies\rm{Volume\:of\:Cube = (side)^3}$

$\implies\rm{Volume\:of\:Cube = (6)^3}$

$\implies\rm{volume\:of\:Cube = 216cm^3}$

Hence, The Volume of Cube is 216cm³

Answer 2

Given:-

• Surface area of a Cube =216sq.cm

To Find:-

• The Volume of Cube.

Solution:-

${\boxed{\rm{\purple{Surface\:area\:of\:Cube= 6(side)^2}}}}$

${\boxed{\rm{\blue{Volume\:of\:cube = (side)^3}}}}$

Now,

$\implies\rm{Surface\:area\:of\:Cube = 6(side)^2}$

$\implies\rm{216sq.cm = 6(side)^2}$

$\implies\rm{(side)^2 = \dfrac{216}{6}}$

$\implies\rm{(side)^2 = 36}$

$\implies\rm{(side = \sqrt{36}}$

$\implies\rm{Side = 6cm}$

Therefore,

$\implies\rm{Volume\:of\:Cube = (side)^3}$

$\implies\rm{Volume\:of\:Cube = (6)^3}$

$\implies\rm{volume\:of\:Cube = 216cm^3}$

Hence, The Volume of Cube is 216cm³