Question

Two cylinders have radii in the ratio 3:5 and heights in the ratio 10:9. Find the ratio of
their volumes.​

Answer 1

Answer:

Suppose that two right circular solid cylinders A with radius r and height h and B with radius R and height Hthen

Ratio of radii r:R=3:5

Let r=3x and R=5x

Ratio of heights =h:H=2:3

Let h=2y and H=3y

Curved Surface Area of cylinder A=2πrh=2π(3x)(2y)=12πxy

Curved Surface Area of cylinder B=2πRH=2π(5x)(3x)=30πxy

Ratio of their Curved Surface Area of A and B=

30πxy

12πxy

=

5

2

Hence, the ratio of the curved surface areas of cylinders is 2:5.

Volume of cylinder A=πr

2

h=π(3x)

2

(2y)=18πx

2

y

Volume of cylinder B=πR

2

H=π(5x)

2

(3y)=75πx

2

y

Ratio of the Volume of A and B=

75πx

2

y

18πx

2

y

=

25

6

Hence, the ratio of the volumes of cylinders is 6:25.

Hope this helps you mate!