Question

use structure. nicole designs a jewelry box in the shape of a right rectangular prism. The height is 2 inches . the length is three times as long as the height, and the width is twice as long as the height. if the box needs to have a volume greater than 50 cubic inches, will her design work? Why or why not?

Answer 1

Let's calculate the volume of the jewelry box based on the given dimensions and see if it meets the requirement of having a volume greater than 50 cubic inches.

The height of the jewelry box is 2 inches.

1. Length (L): "three times as long as the height" means L = 3 * 2 = 6 inches.

2. Width (W): "twice as long as the height" means W = 2 * 2 = 4 inches.

Now, we can calculate the volume (V) of the rectangular prism using the formula:

V = L × W × H

Plugging in the values we found:

V = 6 × 4 × 2 = 48 cubic inches

So, based on Nicole's design, the jewelry box has a volume of 48 cubic inches, which is less than the required 50 cubic inches. Therefore, her design will not work because it does not meet the requirement of having a volume greater than 50 cubic inches.