Question

Cube A has a volume of 9 in3. Cube B has a volume of 5 in3. Which of the following expresses the ratio of the side length of Cube A to the side length of Cube B?
(A) 3 : 5 ^1/3
(B) 5^1/3 : 3^1/3
(C) 3^1/3 : 5^2/3
(D) 3^1/3 : 5^1/3
(E) 3^2/3 : 5^1/3

Answer 1

Using the formula for the volume of a cube, it is found that the expression which gives the ratio of the side length of Cube A to the side length of Cube B is:

$r = \frac{3^{\frac{2}{3}}}{5^{\frac{1}{3}}}$

Which means that option E is correct.

The volume of a cube of side length l is given by:

$V = l^3$

For Cube A, the volume is of 9 cubic inches, hence:

$l_a^3 = 9$

$l_a = \sqrt[3]{9}$

$l_a = 9^{\frac{1}{3}}$

$l_a = 3^{\frac{2}{3}}$

For Cube B, the volume is of 5 cubic inches, hence:

$l_b^3 = 5$

$l_b = \sqrt[3]{5}$

$l_b = 5^{\frac{1}{3}}$

Then, the ratio is:

$r = \frac{l_a}{l_b} = \frac{3^{\frac{2}{3}}}{5^{\frac{1}{3}}}$

To learn more about the volume of a cube, you can take a look at brainly.com/question/13030328