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(D) Let the radius and the height be $r$ and $h$ respectively.The curved surface area of a cylinder is $2 \pi rh$.The curved surface area of a cone is

Vedclass · Accepted Answer

$3:4$

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(D) Let the radius and the height be $r$ and $h$ respectively.The curved surface area of a cylinder is $2 \pi rh$.The curved surface area of a cone is $\pi rl$,where $l = \sqrt{h^2 + r^2}$.Given the ratio of their curved surface areas is $8:5$:$\frac{2 \pi rh}{\pi r \sqrt{h^2 + r^2}} = \frac{8}{5}$$\frac{2h}{\sqrt{h^2 + r^2}} = \frac{8}{5}$$\frac{h}{\sqrt{h^2 + r^2}} = \frac{4}{5}$Squaring both sides:$\frac{h^2}{h^2 + r^2} = \frac{16}{25}$$25h^2 = 16h^2 + 16r^2$$9h^2 = 16r^2$$\frac{r^2}{h^2} = \frac{9}{16}$$\frac{r}{h} = \frac{3}{4}$Thus,the ratio of their radius and height is $3:4$.

$A$ 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

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