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A right circular cylinder and a right circular cone have equal bases and equal heights. If their curved surface areas are in the ratio $8: 5$, then find the ratio between the radius of their bases to their height.
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Let $r$ and $h$ be the radius and height of cylinder as well as cone respectively
$\frac{2\pi rh}{\pi r l} = \frac{8}{5}$ (I) (1 Mark)
$\Rightarrow \frac{2h}{\sqrt{r^2+h^2}} = \frac{8}{5}$
$\Rightarrow 100 h^2 = 64 r^2 + 64 h^2$
$\Rightarrow 36 h^2 = 64 r^2$ (II) (1 Mark)
$\therefore \frac{r}{h} = \frac{3}{4}$ (III) (1 Mark)
Hence the required ratio is $3: 4$
$\frac{2\pi rh}{\pi r l} = \frac{8}{5}$ (I) (1 Mark)
$\Rightarrow \frac{2h}{\sqrt{r^2+h^2}} = \frac{8}{5}$
$\Rightarrow 100 h^2 = 64 r^2 + 64 h^2$
$\Rightarrow 36 h^2 = 64 r^2$ (II) (1 Mark)
$\therefore \frac{r}{h} = \frac{3}{4}$ (III) (1 Mark)
Hence the required ratio is $3: 4$