Question

Find the ratio of sides of cubes whose volumes are 729 and 512 respectively.

• A. 9:16
• B. 9:8
• C. 16:9
• D. 8:9

Answer 1

The correct option is B 9:8

Volume of a cube = (Side of the cube)${}^3$
Side of the cube = $\sqrt[3]{3\text{Volume of the cube}}$
Sides of the cubes whose volumes are 729 and 512 respectively are $\sqrt[3]{3729}$ and $\sqrt[3]{3512}$.

$\therefore$ Ratio of sides
= $\sqrt[3]{3729}$:$\sqrt[3]{3512}$
=$\sqrt[3]{39\times 9\times 9}$:$\sqrt[3]{38\times 8\times 8}$
= $\sqrt[3]{39^3}$:$\sqrt[3]{38^3}$
= 9:8

Hence, ratio of the sides is 9:8.