Question

Two right circular cylinders of equal volume have their heights in the ratio of $4:9$. Find the ratio of their curved surface areas.

• A. $9:4$
• B. $2:3$
• C. $4:9$
• D. $3:2$

Answer 1

The correct option is B $2:3$

$V_1=V_2$

$\Rightarrow \pi r^2{h}_1=\pi r^2{h}_2,let{h}_1=4x\&h_2=9x$

$\Rightarrow \frac{R^2}{r^2}=\frac{h_2}{h_1}=\frac{9x}{4x}\Rightarrow \frac{R}{r}=\sqrt{\frac{9}{4}}=\frac{3}{2}$

Now, $\frac{S_1}{S_2}=\frac{2\pi R{h}_1}{2\pi r{h}_2}=\frac{3}{2}\times \frac{4x}{9x}=\frac{2}{3}or2:3$