Question

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?

Answer 1

Answer:

192 unit cubes.

Step-by-step 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.

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

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

$\text{Volume of cube}=\frac{1^3}{4^3}\text{ unit}^3$

$\text{Volume of cube}=\frac{1}{64}\text{ unit}^3$

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

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

$n\times \frac{1}{64}\text{ Unit}^3=3\text{ Unit}^3$

$n\times \frac{1}{64}=3$

$n\times \frac{1}{64}\times 64=3\times 64$

$n=192$

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

Answer 2

Answer:

192 cubes

Step-by-step explanation: