Question

A cylinder and a cone have equal base radii and equal heights. If their curved surface areas are in the ratio $8:5$, what is the ratio of their radii to heights?

• A. $8:5$
• B. $4:3$
• C. $3:4$
• D. $5:8$

Answer 1

The correct option is C $3:4$

C.S.A of cyl. = $2\pi rh$

C.S.A. of cone = $\pi r\ell =\pi r\sqrt{h^2+r^2}$

As $\frac{C.S.Aofcyl}{C.S.Aofcone}=\frac{8}{5}$

$\Rightarrow \frac{2\pi rh}{\pi r\sqrt{h^2+r^2}}=\frac{8}{5}$

$\frac{h}{\sqrt{h^2+r^2}}=\frac{4}{5}$ (square both side)

$\Rightarrow 25h^2=16(h^2+r^2)$

$\Rightarrow 9h^2=16r^2$

$\Rightarrow \frac{h}{r}=\frac{4}{3}$

$\Rightarrow \frac{r}{h}=\frac{3}{4}$