Question

Find the maximum volume of a cone that can be out of a solid hemisphere of radius $r$.

Answer 1

We have radius of Hemisphere is r.

Radius of Hemisphere = Radius of Cone

and

Radius of Hemisphere = Height of Cone

h = r.....(equation 1)

We know that maximum volume of the cone (V) is = (1/3)πr²h

i.e,

$V=\frac{1}{3}\times \pi r^3$cubic units

Thus the maximum volume of cone is $\frac{1}{3}\times \pi r^3$cubic units when take out from solid hemisphere of radius r.