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Question

# The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 3. The ratio of their curved surface areas is __________.

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Solution

## Let r1 be the radius and h1 be the height of first cylinder & r2 be the radius and h2 be the height of second cylinder. $\therefore \frac{{r}_{1}}{{r}_{2}}=\frac{2}{3}$ and $\frac{{h}_{1}}{{h}_{2}}=\frac{5}{3}$ .....(1) (Given) Now, $\frac{\mathrm{Curved}\mathrm{surface}\mathrm{area}\mathrm{of}\mathrm{first}\mathrm{cylinder}}{\mathrm{Curved}\mathrm{surface}\mathrm{area}\mathrm{of}\mathrm{second}\mathrm{cylinder}}$ $=\frac{2\mathrm{\pi }{r}_{1}{h}_{1}}{2\mathrm{\pi }{r}_{2}{h}_{2}}$ $=\frac{{r}_{1}}{{r}_{2}}×\frac{{h}_{1}}{{h}_{2}}$ $=\frac{2}{3}×\frac{5}{3}$ [Using (1)] $=\frac{10}{9}$ ∴ Curved surface area of first cylinder : Curved surface area of second cylinder = 10 : 9 Thus, the ratio of the curved surface areas of the two cylinders is 10 : 9. The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 3. The ratio of their curved surface areas is ___10 : 9___.

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