Question

What is the volume of a cube with a surface area of 54 square units?

• A. 18
• B. 27
• C. 36
• D. 45
• E. 64

Hint:

For a cube, remember the formulas for surface area \( A = 6s^2 \) and volume \( V = s^3 \). Once you find the side length, you can easily calculate the volume.

Answer 1

The Correct Option is B

The surface area \( A \) of a cube is given by the formula: \[ A = 6s^2, \] where \( s \) is the length of a side of the cube. We are told the surface area is 54 square units, so we have: \[ 6s^2 = 54. \] Now, divide both sides by 6: \[ s^2 = 9. \] Take the square root of both sides: \[ s = 3. \] The volume \( V \) of a cube is given by the formula: \[ V = s^3. \] Substitute \( s = 3 \) into the volume formula: \[ V = 3^3 = 27. \] Thus, the volume of the cube is \( V = 27 \) cubic units.