Question

A right rectangular prism's edge lengths are 4 1 2 inches, 4 inches, and 3 inches. How many unit cubes with edge lengths of 1 3 inch can fit inside the prism?

Answer 1

Question:

A right rectangular prism's edge lengths are  $4\frac{1}{2}$ inches, 4 inches, and 3 inches. How many unit cubes with edge lengths of $\frac{1}{3}$ inch can fit inside the prism?

Answer:

1458 cubes with edge lengths of  $\frac{1}{3}$ inch can fit inside the prism.

Step-by-step explanation:

Given:

Dimensions of the rectangular prism = $4\frac{1}{2}$ inches, 4 inches, and 3 inches

length of  Edge of the cube = $\frac{1}{3}$

To Find:

Number of unit cubes that can fit inside the prism =?

Solution:

Step 1: Finding the volume of the right rectangular prism

Volume of the right Rectangular prism is = $w\times h\times l$

where

w = width of theright Rectangular prism

h = height of the right Rectangular prism

l = lenght of the right Rectangular prism

Substituting the values ,

Volume of the right Rectangular prism is = $4\frac{1}{2}\times4\times 3$

Volume of the right Rectangular prism is = $\frac{9}{2}\times4\times 3$

Volume of the right Rectangular prism is = $4.5\times4\times 3$

Volume of the right Rectangular prism is = 54 $inch^3$

Step 2: Finding the volume of the cube

Volume of the cube = $(edge)^3$

Substituting the  values,

Volume of the cube = $( \frac{1}{3})^3$

Volume of the cube = $( \frac{1}{27})$

Step 3: Find the number of cube that can fit in the cube.

Number of  cubes = $\frac{\text{volume of the right Rectangular prism}}{\text{Volume of the cube}}$

Number of  cubes = $\frac{54}{\frac{1}{27}}$

Number of  cubes = $54\times27$

Number of  cubes  =  1458 cubes