Home » Test Prep » ACT Section 2: Math » What is the surface area of the cube?
The ratio of the number of cubic units in the volume of a cube to the number of square units in the surface area of the cube is 2:3. What is the surface area of the cube?
A. 16 square units
B. 24 square units
C. 64 square units
D. 96 square units
E. 144 square units
Correct Answer: D
Explanation/Reference:
Explanation:
The volume of a cube is equal to e3, where e is the length of an edge of the cube. The surface area of a cube is equal to 6e2. If the ratio of the number of cubic units in the volume to the number of square units in the surface area is 2:3, then three times the volume is equal to two times the surface area: 3e3 = 2 x 6e2
3e3 = 12e2
3e = 12 e = 4The edge of the cube is four units and the surface area of the cube is 6 x 42 = 96 square units.
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