The perimeter of one face of a cube is 36 cm. What is its volume?

Correct option is D

Given:

The perimeter of one face of a cube is 36 cm.

Formula Used:

The perimeter of a square face is given by:

Perimeter = $$4 \times \text{side length}$$​

From this, we can solve for the side length s:

s =$$\frac{\text{Perimeter}}{4}$$​

The volume of a cube is given by:

​$$\text{Volume} = \text{side length}^3$$​

Solution:
Since the perimeter of one face is 36 cm, the side length s is:

s =$$\frac{\text{Perimeter}}{4} = \frac{36}{4} = 9 \, \text{cm}$$​

The volume is the cube of the side length:

Volume = $$9^3 = 9 \times 9 \times 9 = 729 \, \text{cm}^3$$​
The volume of the cube is 729 cm³.