Question

The perimeter of one face of a cube is 24cm, its volume must be :

• A. 216 cm³
• B. 1200 cm³
• C. 576 cm³
• D. 13824 cm³

Answer 1

The Correct Option is A

The problem requires us to determine the volume of a cube given that the perimeter of one face is 24 cm. A cube has six faces, each a square, and the perimeter of a square is four times the side length. Therefore, if the perimeter of one face is 24 cm, we use the formula:

P = 4s

where P is the perimeter, and s is the side length. Substituting the given perimeter:

24 = 4s

Solving for s:

s = 24/4 = 6 cm

Next, the volume V of a cube is calculated as:

V = s³

Substituting the side length:

V = 6³ = 6 × 6 × 6 = 216 cm³

The volume of the cube is therefore 216 cm³, which matches the given correct answer option.