Answer in Brief

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

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#### Solution

\[\text{ Let the radii of two cylinders be 2r and 3r, respectively, and their heights be 5h and 3h, respectively .} \]

\[ \text{ Let S_1 and S_2 be the curved surface areas of the two cylinder } . \]

\[ \text{ S_1 = Curved surface area of the cylinder of height 5h and radius 2r } \]

\[ \text{ S_2 = Curved surface area of the cylinder of height 3h and radius 3r} \]

\[ \therefore S_1 : S_2 = 2 \times \pi \times r \times h : 2 \times \pi \times r \times h\]

\[ = \frac{2 \times \pi \times 2r \times 5h}{2 \times \pi \times 3r \times 3h} \]

\[ = 10 : 9\]

Concept: Surface Area of Cylinder

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