Question

sally received an amazon package in the mail today. the box was in the shape of a cube and its volume was 512 inches cubed. given this volume what is the area of the bottom of the box (only one side)?

Explanation:

Step1: Find the side length of the cube

The volume formula of a cube is \(V = s^{3}\), where \(s\) is the side - length. Given \(V = 512\) cubic inches. Then \(s=\sqrt[3]{V}\).

$$s=\sqrt[3]{512}=\sqrt[3]{8\times8\times8}=8$$

Step2: Calculate the area of the bottom of the cube

The area of one side (bottom) of a cube is \(A=s^{2}\). Since \(s = 8\) inches.

$$A=8^{2}=64$$

Answer:

64