The radii of two cylinders are in the ratio 5: 7 and their heights are in the ratio 3: 5 .what is the ratio of their curved surface area?

Given,
Two cylinders whose radii are in ratio 5:7 and height in the ratio 3:5.
Let the radius of the first cylinder be

r 1

, height of first cylinder be

h 1

, the radius of the second cylinder be

r 2

and height of second cylinder be

h 2

.
According to question,

r 1 r 2 = 57

and

h 1 h 2 = 35

The curved surface area of first cylinder is

C S A 1 = 2 π r 1 h 1

.
The curved surface area of second cylinder is

C S A 2 = 2 π r 2 h 2

.
The ratio of the curved surface areas is given by

C S A 1 C S A 2 = 2 π r 1 h 1 2 π r 2 h 2 ⇒ C S A 1 C S A 2 = r 1 r 2 × h 1 h 2 ⇒ C S A 1 C S A 2 = 57 × 35 ⇒ C S A 1 C S A 2 = 37

Therefore, the ratio of the curved surface of the cylinders is 3:7.
Hence, the correct option is 1.

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