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A rectangular prism with a volume of 333 cubic units is filled with cubes with side lengths of \dfrac14 4 1 ​ start fraction, 1, divided by, 4, end fraction unit. How many \dfrac14 4 1 ​ start fraction, 1, divided by, 4, end fraction unit cubes does it take to fill the prism?

2 Answers

7 votes

Answer:

192 cubes

Explanation:

User Mariana Soffer
by
8.6k points
3 votes

Answer:

192 unit cubes.

Explanation:

Let n represent number of cubes with each side 1/4 unit.

We have been given that a rectangular prism with a volume of 3 cubic units is filled with cubes with side lengths of 1/4 unit. We are asked to find the number of cubes that will fill that prism.

First of all, we will find volume of each cube.


\text{Volume of cube}=\text{Side length}^3


\text{Volume of cube}=((1)/(4)\text{ unit})^3


\text{Volume of cube}=(1^3)/(4^3)\text{ unit}^3


\text{Volume of cube}=(1)/(64)\text{ unit}^3

The volume of rectangular prism will be equal to volume of n cubes.


\text{Volume of n cubes}=\text{Volume of rectangular prism}


n* (1)/(64)\text{ Unit}^3=3\text{ Unit}^3


n* (1)/(64)=3


n* (1)/(64)* 64=3* 64


n=192

Therefore, it will take 192 unit cubes to fill the prism.

User Himanshu Sharma
by
8.0k points
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