How many LaTeX: \frac{1}{3}1 3 inch cubes does it take to fill a box with width LaTeX: 2\frac{2}{3}2 2 3 inches, length LaTeX: 3\frac{1}{3}3 1 3 inches, and height LaTeX: 2\frac{1}{3}2 1 3 inches?

186.7 cubes

Step-by-step explanation:

How many LaTeX: \frac{1}{3}1 3 inch cubes does it take to fill a box with width LaTeX: 2\frac{2}{3}2 2 3 inches, length LaTeX: 3\frac{1}{3}3 1 3 inches, and height LaTeX: 2\frac{1}{3}2 1 3 inches?

Step 1

We find the volume of the box

= Length × Width × Height

Length = 3 1/3 inches = 10/3 inches

Width = 2 2/3 inches = 8/3 inches

Height = 2 1/3 inches = 7/3 inches

The volume of the box =

10/3 inches × 8/3 inches × 7/3 inches

= 560/9 cubic Inches

= 62 2/9 cubic inches

Step 2

How many 1/3 inch cubes would fill the box.

This is calculated as:= 62 2/9 cubic inches/ 1/3 inches

= 560/9 ÷ 1/3

= 560/9 × 3/1

= 186.66666667 cubes

Approximately = 186.7 cubes

17 1/3

step-by-step explanation: