# 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 volumes and the ratio of their curved surfaces. - Mathematics

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Sum

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 volumes and the ratio of their curved surfaces.

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#### Solution

Data given is as follows:

Ratio of radii of two cylinders = 2:3

Ratio of heights of two cylinders = 5:3

We have to find out the following:

(i) Ratio of the volumes of the two cylinders

(ii) Ratio of the Curved Surface Area of the two cylinders

Let r_1and r_2be the radii of the two cylinders respectively.

Let h_1 and h_2be the heights of the two cylinders respectively.

Therefore we have,

r_1/r_2 = 2/3

h_1/h_2 = 5/3

(i) Since we have to find the ratio of the volumes of the two cylinders, we have

("Volume of cylinder 1")/("Volume of cylinder 2") = (pi r_1^2h_1)/(pir_2^2h_2)

=(r_1/r_2)^2 (h_1/h_2)

=(2/3)^2 (5/3)

("Volume of cylinder 1")/("Volume of cylinder 2") = (20/27)

(ii) Since we have to find the ratio of the curved surface areas of the two cylinders, we have,

("Curved Surface Area of cylinder 1")/("Curved Surface Area if cylinder 2") = (2pir_1h_1)/(2pir_2h_2)

=(r_1/r_2) (h_1/h_2)

=(2/3)(5/3)

("Curved Surface Area of cylinder 1")/("Curved Surface Area if cylinder 2") = (10/9)

Concept: Surface Area of Cylinder
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#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 19 Surface Areas and Volume of a Circular Cylinder
Exercise 19.2 | Q 9 | Page 21

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