Question

the volume of cube a is 8 cubic inches. the face of cube b has an area of 121 square inches. which cube has a greater side length? the side length of cube a is inches. the side length of cube b is inches. cube b has a greater side length. (simplify your answers.)

Explanation:

Step1: Find side - length of Cube A

The volume formula for a cube is $V = s^3$, where $V$ is volume and $s$ is side - length. Given $V_A=8$ cubic inches, then $s_A=\sqrt[3]{V_A}$. So, $s_A = \sqrt[3]{8}=2$ inches.

Step2: Find side - length of Cube B

The area of one face of a cube is $A = s^2$, where $A$ is the face - area and $s$ is side - length. Given $A_B = 121$ square inches, then $s_B=\sqrt{A_B}$. So, $s_B=\sqrt{121}=11$ inches.

Step3: Compare side - lengths

Since $2<11$, Cube B has a greater side - length.

Answer:

The side length of Cube A is 2 inches. The side length of Cube B is 11 inches. Cube B has a greater side length.