Question

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 1

8320 cubes

Explanation:

First we need to find the volume of the rectangular prism.

The formula to get the volume is:

`V = LWH`

The variables of our prism are:

`L=20 in\\W=2in\\H=3(1)/(4)`

We simply plug in our values into the formula.

`V=LWH`

`V=20*2*3(1)/(4)`

`V=130in^(3)`

Now we need to figure out the volume of the cubes.

The formula to get the volume is:

`V = s^3`

`V = 1/4^3`

`V = 0.015625in^3`

Now that we have the volume of both the prism and the cubes, we then just divide the volume of the prism to the volume of the cube.

`(130)/(0.015625)`

= 8320 cubes

Answer 2

Answer: 8320 cubes.

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=((1)/(4)in)^(3)=(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=(V_1)/(V_2)=(130in^(3))/(0.0156in^(3))=8320` cubes