Question

a cube has a volume of 512 inches cubed. what is the surface area of the cube? select one answer: 64 inches squared, 384 inches squared, 264 inches squared, 1,024 inches squared

Explanation:

Step1: Find cube edge length

Volume of cube $V = s^3$, so $s = \sqrt[3]{V}$. Given $V=512$ cubic inches:
$$s = \sqrt[3]{512} = 8 \text{ inches}$$

Step2: Calculate surface area

Surface area of cube $SA = 6s^2$. Substitute $s=8$:
$$SA = 6 \times 8^2 = 6 \times 64 = 384 \text{ square inches}$$

Answer:

C. 384 inches squared