A solid cylinder is melted and cast into a cone of same radius. The heights of the cone and cylinder are in the ratio (a)   9:1       (b)  1:9         (c)  3:1         (d)  1:3

Explanation

Given : Radius is same for cone and cylinder i.e `r`.

Let the height of cone be h and height of cylinders be H.

Now, Volume of cone = Volume of cylinder

`(1/3)pir^2h = pir^2H`

`3H=h`

`h/H=3/1`

Hence, ratio of the heights of the cone and the cylinder = `3:1`

`therefore` option(c) is correct.