Question

The radii of two circular cylinders are in the ratio 2 : 3 and their heights are in the ratio 3 : 5, find the ratio of their:

1. Volumes 
2. Curved surface areas.

Answer 1

Given

r₁​:r₂​ = 2:3

Height ratio:

h₁​:h₂​ = 3:5

(i) Ratio of volumes

Volume of a cylinder:

V = πr²h

`V_1​:V_2 = r_1^2​h1​: r_2^2​h_2​`

(2)² × 3 : (3)² × 5

4 × 3 : 9 × 5

12:45

Simplify,

Ratio of volumes = 4 : 15

(ii) Ratio of curved surface areas

Curved surface area of a cylinder:

CSA = 2πrh

so,

`CSA_1​:CSA_2 = r_1​h_1​:r_2​h_2​`

Substitute ratios:

2 × 3:3 × 5

6 : 15

2:5

Ratio of curved surface areas = 2 : 5