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

Answer:

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

Step-by-step 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:

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

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

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

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

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

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

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