Answer: 8320 cubes.
Step-by-step explanation:
1. Calculate the volume of the rectangular prism:
[tex]V_1=l*w*h[/tex]
Where l is the lenght, w is the width and h is the height.
Substitute values.
(You can convert 3 1/4 to decimal by dividing the numerator by the denominator of the fraction and add this to the whole part: 3+0.25=3.25)
Then:
[tex]V_1=20in*2in*3.25in=130in^{3}[/tex]
2. Calculate the volume of a cube:
[tex]V_2=s^{3}[/tex]
Where s is the lenght of any side.
Then:
[tex]V_2=(\frac{1}{4}in)^{3}=\frac{1}{64}in^{3}=0.0156in^{3}[/tex]
3. To calculate the number of cubes that are needed to fill the rectangular prism (which you can call n) , you must divide the volume of the prism by the volume of a cube. Then:
[tex]n=\frac{V_1}{V_2}=\frac{130in^{3}}{0.0156in^{3}}=8320[/tex] cubes
