Question

A rectangular 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 1

Answer: 8320 cubes.

Step-by-step explanation:

1. Calculate the volume of the rectangular prism:

$V_1=l*w*h$

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:

$V_1=20in*2in*3.25in=130in^{3}$

2. Calculate the volume of a cube:

$V_2=s^{3}$

Where s is the lenght of any side.

Then:

$V_2=(\frac{1}{4}in)^{3}=\frac{1}{64}in^{3}=0.0156in^{3}$

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:

$n=\frac{V_1}{V_2}=\frac{130in^{3}}{0.0156in^{3}}=8320$ cubes

Answer 2

Answer:

8320 cubes. he is right