Question

the radii of 2 cylinders are in the ratio of 2:3 and their heights are in the ratio of 5:3. then , find the ratio of their volumes

Answer 1

hello users ...

solution:-
we know that:
volume of cylinder = πr²h 

Here,
according to given :
Ratio between their radii 2 : 3 
let Radius of first cylinder = 2r
And
let Radius of second cylinder = 3r

Also,
The ratio between their height 5 : 3
let the height of first cylinder = 5h
And
let height of second cylinder = 3h

Now,
volume of first cylinder = πr²h

= π (2r)² 5h 
= π×(4r² )× 5h 
= 20 × πr²h 

And
the volume of second cylinder = πr²h

= π (3r)² 3h 
= π×(9r²)×3h 
= 27 × πr²h

Now,
Required Ratio = volume of first cylinder / volume of second cylinder

= 20 πr²h / 27 πr²h 
= 20 / 27 = 20 : 27 Answer 

# hope it helps  :)