A cone, a hemisphere and a cylinder stand on equal bases and have the same height. Show that their volumes are in the ratio 1:2:3.

Explanation

True
Let radius of hemisphere is r.
Volume of a cone, `V_(1) =(1)/(3) pir^(2)h`
`" "V_(1) = (1)/(3) pir^(2)(r)" "[because h= r]`
`rArr " " =(1)/(3) pir^(3)`
Now, Volume of a hemisphere,`V_(2) = (2)/(3) pir^(3)`
and Volume of cylinder ,`V_(3) = pir^(3) h = pir^(2) xx r = pir^(3)" "[because h =r]`
`therefore" "V_(1): V_(2): V_(3)+ (1)/(3)pir^(3): (2)/(3) pir^(3) : pir^(3) = 1: 2:3`
Hence, the raio of thier volumes is 1: 2: 3.