If the radius of the cylinder is 4 units, what is the surface area of the cube?

The length of an edge of a cube is equal to half the height of a cylinder that has a volume of 160π cubic units.

If the radius of the cylinder is 4 units, what is the surface area of the cube?
A . 64 square units
B . 96 square units
C . 100 square units
D . 125 square units
E . 150 square units

Answer: E

Explanation:

The volume of a cylinder is equal to πr2h. The volume of the cylinder is 160π and its radius is 4. Therefore, the height of the cylinder is equal to:

160π = π × 4 2 × h

160 = 16h

h = 10

The length of an edge of the cube is equal to half the height of the cylinder. The edge of the cube is 5 units. The surface area of a cube is equal to 6e2, where e is the length of an edge of the cube. The surface area of the cube = 6 × 5 2 = 6 × 25 = 150 square units.