Question

If the perimeter of one face of a cube is 40cm then it's volume is

Answer 1

let the side of cube be a.

perimeter of one side=4a=40cm
a=10cm.

volume of cube=a*a*a

=10*10*10=1000 cm^3.

done.

Answer 2

Given data: Perimeter of one face of a cube is 40cm.

To Find: The volume of a cube.

Solution:

Cube consists of six square faces.

The formula for perimeter of a square is 4a.

Hence, the perimeter of each face of a cube is 4a, since it has one side of a length as 'a' units.

Consider the given statement, perimeter of one face of a cube is 40cm.

$4a=40$ $cm$

$a=\frac{40}{4}$

$a=10$ $cm$.

Thus, the length of one side of a cube 'a' is 10cm.

Volume of a cube = (side)³

Here side = a,

Volume of a cube = $a^{3}$

Substitute, a =10cm

Volume of a cube = $10^{3}$  

$=10$×$10$×$10$

$=1000$ $cm^{3}$.

Therefore, the volume of a cube is 1000 $cm^{3}$.