Question

If the volumes of two cubes are in the ratio 64: 125, then what is the ratio of the lengths of their edges?

• A. 8:5
• B. 2:25
• C. 4:25
• D. 4:5

Answer 1

The correct option is D

4:5

Let the first cube has an edge $a_1$ whereas the second cube has edge $a_2$
Given,
$\frac{\text{Volume of first cube}}{\text{Volume of second cube}}=\frac{64}{125}$
$\Rightarrow \frac{a_1^3}{a_2^3}=\frac{64}{125}$
$\Rightarrow \frac{a_1}{a_2}=\frac{4}{5}$
Thus the ratio of the lengths of the edges of the two cubes is 4:5.