Question

How many \frac{1}{3} 3 1 ​ inch cubes does it take to fill a box with width 22 \frac{2}{3} 3 2 ​ inches, length 33 \frac{1}{3} 3 1 ​ inches, and height 22 \frac{1}{3} 3 1 ​ inches?

Answer 1

560

Explanation:

First we need to find the volume of the cube;

Volume = Length * Width * height

Given;

Length = 3 1/3 in

Width = 2 2/3 in

Height = 2 1/3 in

Volume = 3 1/3 * 2 2/3 * 2 1/3

Volume = 10/3 * 8/3 * 7/3

Volume = 560/3 in^3

To know thw amount of 1/3 in^3 it takes to fill the box, we will take the ratio of the volume to the unit volume;

Ratio = 560/3÷1/3

Ratio = 560/3 * 3/1

Ratio = 560

Hence it will take 560 1/3 in^3 to fill a box with that volume