Question:
A right rectangular prism's edge lengths are [tex]4\frac{1}{2}[/tex] inches, 4 inches, and 3 inches. How many unit cubes with edge lengths of [tex]\frac{1}{3}[/tex] inch can fit inside the prism?
Answer:
1458 cubes with edge lengths of [tex]\frac{1}{3}[/tex] inch can fit inside the prism.
Step-by-step explanation:
Given:
Dimensions of the rectangular prism = [tex]4\frac{1}{2}[/tex] inches, 4 inches, and 3 inches
length of Edge of the cube = [tex]\frac{1}{3}[/tex]
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 = [tex]w\times h\times l[/tex]
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 = [tex]4\frac{1}{2}\times4\times 3[/tex]
Volume of the right Rectangular prism is = [tex]\frac{9}{2}\times4\times 3[/tex]
Volume of the right Rectangular prism is = [tex] 4.5\times4\times 3[/tex]
Volume of the right Rectangular prism is = 54 [tex]inch^3[/tex]
Step 2: Finding the volume of the cube
Volume of the cube = [tex](edge)^3[/tex]
Substituting the values,
Volume of the cube = [tex]( \frac{1}{3})^3[/tex]
Volume of the cube = [tex]( \frac{1}{27})[/tex]
Step 3: Find the number of cube that can fit in the cube.
Number of cubes = [tex]\frac{\text{volume of the right Rectangular prism}}{\text{Volume of the cube}}[/tex]
Number of cubes = [tex]\frac{54}{\frac{1}{27}}[/tex]
Number of cubes = [tex]54\times27[/tex]
Number of cubes = 1458 cubes
