Question

Gina wrapped a present in a box with volume 343 in³. What are the side lengths of the box wrapped?

A) Side lengths: 7 in, 7 in, 7 in
B) Side lengths: 9 in, 9 in, 4 in
C) Side lengths: 14 in, 7 in, 2 in
D) Side lengths: 11 in, 11 in, 3 in

Answer 1

The side lengths of the box with a volume of 343 in³ are 7 in, 7 in, 7 in, because the cube root of 343 is 7.

Step-by-step explanation:

The student is attempting to determine the side lengths of a box that has a known volume of 343 cubic inches. To find the side lengths of a cubic box (a box where all sides are equal), we take the cube root of the volume. Since the cube root of 343 is 7, the side lengths of the box are each 7 inches.

Therefore, the correct answer is:
A) Side lengths: 7 in, 7 in, 7 in

This is because the volume of a cubic box is calculated by multiplying the length by the width by the height, which in this case would be 7×7×7 = 343 in³.