Question

If the ratio of radii of two cylinders of same height is 4:5, then show that the ratio of their curved surface area 4:5 and the ratio of their volume is 16:25

Answer 1

Let r1 and r2 be radii of two cyclinder and V1, V2  be their volume . 

 

Let h be height of the two cyclinders, then  

 

 V1 = πr2h and V2  =  πr22h 

 

∴  V1 /  V2 =  πr12h /  πr22h  = r12 / r22 = 16 / 25 . 

 

There's an alternate method too:

 

 

ratio of radii = 4:5

ratio of CSA= 4:5 ( to show)

ratio of volume= 16:25( to show) 

let height be h 

then the CSA = 2πr h/ 2πrh

from here we get = 4:5

 

same in volume = πr²h / πr²h

= 4²/5²

= 16: 25 

 

Hope This Helps :)