# The radii of two cylinders are in the ratio of 2:3 and their heights are in the ratio of 5:3. The ratio of their volumes is:

a. 10 : 17

b. 20 : 27

c. 17 : 27

d. 20 : 37

**Solution:**

Given, the radii of two cylinder are in the ratio 2 : 3

The heights are in the ratio 5 : 3

We have to find the ratio of their volumes.

Let the radii of two cylinders be 2r and 3r

Let the heights of the two cylinders be 5h and 3h

Volume of the cylinder = πr²h

Where, r is the radius of the cylinder

h is the height of the cylinder

Volume of cylinder with radius 2r and height 5h = π(2r)²(5h)

= π(4r²)(5h)

= 20πr²h

Volume of cylinder with radius 3r and height 3h = π(3r)²(3h)

= π(9r²)(3h)

= 27πr²h

Ratio of the volume = 20πr²h / 27πr²h

= 20/27

Therefore, the required ratio is 20 : 27

**✦ Try This: **The radii of two cylinders are in the ratio of 3:1 and their heights are in the ratio of 2:3. The ratio of their volumes is

**☛ Also Check: **NCERT Solutions for Class 9 Maths Chapter 13

**NCERT Exemplar Class 9 Maths Exercise 13.1 Problem 6**

## The radii of two cylinders are in the ratio of 2:3 and their heights are in the ratio of 5:3. The ratio of their volumes is: a. 10 : 17, b. 20 : 27, c. 17 : 27, d. 20 : 37

**Summary:**

The radii of two cylinders are in the ratio of 2:3 and their heights are in the ratio of 5:3. The ratio of their volumes is 20 : 27

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