The height of a cone is 40 cm. A small cone is cut off at the top by a plane parallel to its base. If the volume of a small cone is `1/64` of the volume of the given cone, at what height above the base is the section made?

Explanation

`h/H = r/R = l/L`

volume of small cone= `1/3 pi r^2 h`

volume of bigger cone =`1/3 pi R^2 H`

Now, `1/3 pi R^2 H xx 1/64 = 1/3 pi r^2 h`

`(r^2H)/64 = r^2 h`

`h/40 = r/R`

`r= (hR)/40`

now, `(R^2H)/64 = (hR/40)^2 xx h`

...