Question

The total surface area of a cube is 384 cm² ∴ The volume of the cube is ______.

Options

• 64 cm³

• 125 cm³

• 512 cm³

• 729 cm³

Answer 1

The total surface area of a cube is 384 cm² ∴ The volume of the cube is 512 cm³.

Explanation:

Step 1: Formula for the total surface area of a cube

The total surface area A of a cube with side length s is given by:

A = 6s²

We are given that the total surface area is 384 cm²:

6s² = 384

Step 2: Solve for the side length s

s² = `384/6` = 64

s = `sqrt(64)` = 8 cm

Step 3: Find the volume of the cube

The volume V of a cube is given by:

V = s³

Substitute s = 8:

V = 8³ = 512 cm³