Question

A right circular cylinder and a right circular cone have equal base and bases and equal heights If their curved surfaces are in the ratio $8:5$, what is ratio of their base is to their heights ?

• A. $3:4$
• B. $5:4$
• C. $6:7$
• D. $9:8$

Answer 1

The correct option is A $3:4$

$\frac{2\pi rh}{\pi rl}=\frac{8}{5}$ or $l:h=5:4$

Now,$l^2=h^2+r^2$
or $25x^2=16x^2+r^2$
or $r=3x$
$\therefore \frac{r}{b}=\frac{3x}{4x}=\frac{3}{4}$