Question

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.

 

Answer 1

\[\text{ Let the radii of two cylinders be 2r and 3r, respectively, and their heights be 5h and 3h, respectively .}  \]
\[ \text{ Let S_1 and S_2 be the curved surface areas of the two cylinder } . \]
\[ \text{ S_1 = Curved surface area of the cylinder of height 5h and radius 2r } \]
\[ \text{ S_2 = Curved surface area of the cylinder of height 3h and radius 3r} \]
\[ \therefore S_1 : S_2 = 2 \times \pi \times r \times h : 2 \times \pi \times r \times h\]
\[ = \frac{2 \times \pi \times 2r \times 5h}{2 \times \pi \times 3r \times 3h} \]
\[ = 10 : 9\]