Question

A rectangular prism with a volume of 666 cubic units is filled with cubes with side lengths of \dfrac12 2 1 ​ start fraction, 1, divided by, 2, end fraction unit. How many \dfrac12 2 1 ​ start fraction, 1, divided by, 2, end fraction unit cubes does it take to fill the prism?

Answer 1

Answer:

48 cubes.

Step-by-step explanation:

Let n represent number of cubes with each side $\frac{1}{2}$ units.

We have been given that a rectangular prism with a volume of 6 cubic units is filled with cubes with side lengths of $\frac{1}{2}$ units. We are asked to find the number of cubes that will fill the prism.

We know that volume of n cubes will be equal to volume of rectangular prism.

$n\cdot \text{Volume of each cube}=\text{Volume of rectangular prism}$

We also know that volume of a cube with side length 'x' is equal to $x^3$.

$\text{Volume of each cube}=(\frac{1}{2}\text{ Unit})^3$

$\text{Volume of each cube}=\frac{1^3}{2^3}\text{ Unit}^3$

$\text{Volume of each cube}=\frac{1}{8}\text{ Unit}^3$

$n\cdot \frac{1}{8}\text{ Unit}^3=6\text{ Unit}^3$

$n\cdot \frac{1}{8}=6$

$n\cdot \frac{1}{8}\cdot 8=6\cdot 8$

$n=48$

Therefore, it will take 48 cubes with each side $\frac{1}{2}$ units to fill the prism.