Question

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 cube?A. 2

B. 4
C. 8
D.
`\sqrt[3]{4}`
E. 2
`\sqrt[3]{4}`

Answer 1

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.