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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.

Respuesta :

carlosego

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

DizzyBerco

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:

[tex]V = LWH[/tex]

The variables of our prism are:

[tex]L=20 in\\W=2in\\H=3\dfrac{1}{4}[/tex]

We simply plug in our values into the formula.

[tex]V=LWH[/tex]

[tex]V=20*2*3\dfrac{1}{4}[/tex]

[tex]V=130in^{3}[/tex]

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

The formula to get the volume is:

[tex]V = s^3[/tex]

[tex]V = 1/4^3[/tex]

[tex]V = 0.015625in^3[/tex]

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.

[tex]\dfrac{130}{0.015625}[/tex]

= 8320 cubes

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