Question

The volumes of two cylinders are as a : b, and their heights are as 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 $\sqrt{\frac{ad}{bc}}$

$V_1:V_2=a:b$ & $h_1:h_2=c:d$

$\Rightarrow \frac{V_1}{V_2}=\frac{\frac{\pi }{4}{d}_1^2{h}_1}{\frac{\pi }{4}{d}_2^2{h}_2}\Rightarrow \frac{d_1}{d_2}=\sqrt{\frac{ad}{bc}}$