The base radii of two cylinders are in the ratio 2 : 3 and their height are in the ratio 5 : 4.
What is the ratio of their volumes?

Question

The base radii of two cylinders are in the ratio 2 : 3 and their height are in the ratio 5 : 4.What is the ratio of their volumes?

Philoid · Accepted Answer

Given: ratio of base radii of 2 cylinders is 2:3 ie. r₁:r₂

ratio of height of 2 cylinders is 5:4 ie. h₁:h₂

to find : i) ratio of the volumes of 2 cylinders

ii) volume of the second cylinder if first’s volume is 720cm³

procedure :

i)Volume of cylinder = area of base × height

So, Volume of the cylinder = ∏×r²×h

⇒Volume of the first cylinder V1= ∏×(r₁)²×h₁

⇒Volume of the second cylinder V2= ∏×(r₂)²×h₂

So ratio of the volumes of these 2 cylinders =

⇒ =

=

= ×

= (² ×

= ()²×

= ×

=

⇒ =

∴ ratio of volumes of 2 cylinders = 5:9 ie. V₁:V₂