Question

show all work for full credit. 1. the volume of a cube is 216 in³. a. what is the length of the edge of the cube? b. what is the area of one of the faces of the cube?

Explanation:

Step1: Recall volume formula for cube

The volume formula of a cube is $V = s^{3}$, where $s$ is the edge - length. Given $V = 216$ in³, we solve for $s$.
$$s^{3}=216$$

Step2: Solve for edge - length

Take the cube - root of both sides: $s=\sqrt[3]{216}=6$ in.

Step3: Recall area formula for a square face of cube

The area of one face of a cube (which is a square) is $A = s^{2}$. Since $s = 6$ in, then $A=s^{2}=6^{2}=36$ in².

Answer:

a. 6 in
b. 36 in²