A retangular prism has a length of 20 in. a width of 2 in., and a height of 3 1/4 in. The prism is filled with cubes that have edge lengths of 1/4 in. How many cubes are needed to fill the rectangular prism? Enter your answer in the box. To fill the rectangular prism, _______ cubes are needed.

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