# 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. - Mathematics

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.

#### Solution

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

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#### APPEARS IN

RD Sharma Class 8 Maths
Chapter 22 Mensuration - III (Surface Area and Volume of a Right Circular Cylinder)
Exercise 22.1 | Q 7 | Page 10