Question

if the volume of a cube is 8, what is the total surface area of the cube?

(a) 2
(b) 4
(c) 16
(d) 24
(e) 64

Explanation:

Identify the given volume

We are given that the volume of a cube is \(V = 8\).

Find the side length

The volume of a cube with side length \(s\) is given by:

$$V = s^3$$

We solve for \(s\):

$$s^3 = 8 \implies s = \sqrt[3]{8} = 2$$

Calculate the surface area

A cube has 6 identical square faces. The total surface area \(A\) is:

$$A = 6s^2$$

Substitute \(s = 2\) into the formula:

$$A = 6(2)^2 = 6(4) = 24$$

Answer:

• (A) 2
• (B) 4
• (C) 16
• (D) 24 (Correct answer)
• (E) 64