A cone and a hemisphere have equal bases and equal volumes the ratio of their heights is 1:2 (b) 2:1 (c) 4:1 (d) `sqrt(2)\ :\ 1`

Explanation

Let the radius of base of hemisphere and cone, each be `r` unit.
Let the height of the cone be `h` unit.
Volume of the cone`=1/3pir^2h`
Volume of the hemisphere`=2/3pir^3`
`1/3pir^2h=2/3pir^3`(given)
`h=2r`
Height of the cone `=2r unit`

Height of the hemisphere = Radius of the hemisphere `=r`

Ratio of the heights of cone and hemisphere `=2r:r=2:1`