Question

3. For two cylinders ratio of diameters A and B, the ratio of lengths is 3 : 1 and the is 1:2. Calculate the ratio of their volumes.​

Answer 1

Alright so the Diameter ratio of cylinder a & b = 1:2 and Length (height) ratio of cylinder a & b = 3:1

We have to find the volume ratio of cylinder a & b.

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

(h & r are assumed as variables)

So,

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

So,the ratio of their volume is 3:4

Hope this helps!^^

Explanation: