A certain clay cube has volume 64 cubic inches. If a smaller clay cube is formed and has half the volume of the original cube, how many inches long is an edge of the smaller cub…

Question

asked May 18, 2020 219k views

1 Answer

Tom Marthenal · Answer 1 · 2020-05-23T05:45:41+0000

Answer:

E.
$2\sqrt[3]{4}\text{ in}$

Explanation:

Let a represent side length of the smaller cube.

We have been given that a certain clay cube has volume 64 cubic inches.

We will use volume of cube formula to answer our given problem.

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

$64\text{ in}^3=\text{Side length}^3$

Since the smaller clay cube has half the volume of the original cube. So volume of smaller cube would be:

$\frac{64\text{ in}^3}{2}=32\text{ in}^3$

Upon substituting our given values in volume formula, we will get:

$32\text{ in}^3=a^3$

Switch sides:

$a^3=32\text{ in}^3$

Take cube root of both sides:

$\sqrt[3]{a^3}=\sqrt[3]{32\text{ in}^3}$

$a=\sqrt[3]{4* 8\text{ in}^3}$

$a=\sqrt[3]{4}* \sqrt[3]{8\text{ in}^3}$

$a=\sqrt[3]{4}* \sqrt[3]{2^3\text{ in}^3}$

$a=\sqrt[3]{4}* 2\text{ in}$

$a=2\sqrt[3]{4}\text{ in}$

Therefore, the side length of the smaller cube is
$2\sqrt[3]{4}\text{ in}$ and option E is the correct choice.