Question

A cone and a hemisphere have the same base and the same height. Find the ratio between their volumes.

Answer 1

Let the radius of base be 'r' and the height be 'h' 

Volume of cone, `V_c` 

= `1/3pir^2h` 

Volume of hemisphere, `V_h` 

= `2/3pir^3` 

`V_c/V_h = (1/3pir^2r)/(2/3pir^3)` 

`=> V_c/V_h = 1/2`

1 : 2