Question

a cube - shaped box has a volume of 64 cubic inches. what is the area of one of its faces? square inches

Explanation:

Step1: Find the side - length of the cube

The volume formula of a cube is $V = s^3$, where $V$ is the volume and $s$ is the side - length. Given $V = 64$ cubic inches, we solve the equation $s^3=64$ for $s$. Taking the cube - root of both sides, we have $s=\sqrt[3]{64}=4$ inches.

Step2: Calculate the area of one face

The area formula of one face of a cube is $A = s^2$. Since $s = 4$ inches, then $A=4^2 = 16$ square inches.

Answer:

16