Question

If a cube has a total surface area of 96, what is its volume?

• A. 16
• B. 36
• C. 64
• D. 96
• E.

Hint:

To calculate the volume of a cube, first find the side length using the surface area, then cube that value.

Answer 1

The Correct Option is C

Step 1: Relate surface area and side length.
The surface area \( A \) of a cube is given by the formula: \[ A = 6s^2 \] where \( s \) is the side length. Step 2: Solve for the side length.
Substitute the given surface area: \[ 96 = 6s^2 \] Solving for \( s^2 \): \[ s^2 = \frac{96}{6} = 16 \] Thus, \( s = 4 \). Step 3: Calculate the volume.
The volume \( V \) of a cube is given by: \[ V = s^3 \] Substitute \( s = 4 \): \[ V = 4^3 = 64 \] Final Answer: \[ \boxed{64} \]