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

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

Step-by-step 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:

$L=20 in\\W=2in\\H=3\dfrac{1}{4}$

We simply plug in our values into the formula.

$V=LWH$

$V=20*2*3\dfrac{1}{4}$

$V=130in^{3}$

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.

$\dfrac{130}{0.015625}$

= 8320 cubes