Question

For two cylinders a and b the ratio of the diameter is 1 : 2 and the ratio of the length is 3: 1. calculate the ratio of their volumes

Answer 1

Given,

Diameter ratio of cylinder a & b = 1:2

Length (height) ratio of cylinder a & b = 3:1

To find,

Volume ratio of cylinder a & b.

Solution,

Let,

The diameter of cylinder a = 1r

And,the diameter of cylinder b = 2r

The length of cylinder a = 3h

And,the length of cylinder b = h

(Here,h & r are assumed as variables.)

Now,

The radius of cylinder a = 1r/2

The radius of cylinder b = 2r/2 = r

So,

The volume of cylinder a = π × (1r/2)² × 3h = π × 1r²/4 × 3h = 3πr²h/4

The volume of cylinder b = π × (r)² × h = πr²h

Ratio of volume = 3πr²h/4 : πr²h = 3πr²h/4 × 1/πr²h = 3/4 = 3:4

Hence,the ratio of their volume is 3:4

Answer 2

Answer: 3:4 is the answer

Step-by-step explanation:....