Question 61

A cylinder and a cone have equal radii of their bases and equal heights. If their curved surface areas are in the ratio 8 : 5, the ratio of their radius and height is

Solution

$$ \frac{curved surface area of cylinder}{curved surface area of cone } = \frac{8}{5} $$

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

$$ \frac{h}{\sqrt h^2 + \sqrt r^2} = \frac{4}{5} $$

on squaring both sides

$$ \frac{h^2}{\sqrt h^2 + \sqrt r^2} = \frac{25}{16} $$

$$ 1 + \frac{r^2}{h^2} = \frac{25}{16} $$

$$ \frac{r^2}{h^2} = \frac{9}{16} $$

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

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