Question

The volumes of two cylinders are a : b and their heights are c :d. Find the ratio of their diameters.

• A. $\frac{ad}{bc}$
• B. $\frac{a{d}^2}{a{c}^2}$
• C. $\sqrt{\frac{ad}{bc}}$
• D. $\sqrt{\frac{a}{b}\times \frac{c}{d}}$

Answer 1

The correct option is C $\sqrt{\frac{ad}{bc}}$

Let $r_1,r_2$ be the radii of the two cylinders respectively. Let the heights of the two cylinders be cK and dK respectively.
$\therefore \frac{\pi r_1^{2}cK}{\pi r_2^{2}dK}=\frac{a}{b}\Rightarrow \frac{r_1}{r_2}=\sqrt{\frac{ad}{dc}}$