Question

A right rectangular prism's edge lengths are 6 inches, 3 inches, and 3į inches. How many unit cubes with edge tengths of į Inchcan fit inside the prism?A)21 unit cubesB63 unit cubesC)189 unit cubesD)1701 unit cubes

Answer 1

Given:

A right rectangular prism's edge lengths are 6 inches, 3 inches, and 3 1/2 inches.

We will find the number of cubes with edge length = 1/3 inches that can fit inside the prism

We will find the volume of the prism and the volume of the cube, then divide the volume of the prism by the volume of the cube:

`\begin{gathered} Prism\text{ }volume=6*3*3(1)/(2)=63\text{ }in^3 \\ \\ cube\text{ }volume=(1)/(3)*(1)/(3)*(1)/(3)=(1)/(27)\text{ }in^3 \end{gathered}`

So, the number of the cubes will be as follows:

`63/(1)/(27)=63*(27)/(1)=1701`

So, the answer will be option D) 1701 unit cubes