Question

A right rectangular prism's edge lengths are 14 inches, 6 inches, and 3 1/3 inches. How many unit cubes with edge lengths of 2/5 inch can fit inside the prism?

Answer 1

4375 unit cubes

Step-by-step explanation

The volume of a right rectangular prism is given by;

`V=lbh`

We substitute the given dimension to obtain,

`V=14 * 6 * (10)/(3) = 280i {n}^(3)`

The volume of the unit cube with edge lengths

`(2)/(5)`

is

`((2)/(5))^(3) = (8)/(125) {in}^(3)`

To find the number of unit cubes that can fit inside the prism, we divide the volume of the rectangular prism by the volume of the unit cube.

`= (280)/( (8)/(125) )`

`= 4375`