Question

A sphere of maximum volume is cut out from a solid hemisphere of radius 6 cm . Find the volume of the cut out sphere.

Answer 1

Answer:

113.14 is the volume of the sphere

Answer 2

Given:

The radius of the hemisphere = 6 cm

To Find:

The volume of the sphere that is cut from the hemisphere

Solution:

The diameter of the cut sphere = The radius of the hemisphere

The diameter of the cut sphere = 6 cm

So, the radius of the cut sphere = Diameter of the sphere/ 2

⇒ The radius of the cut sphere = 6/2 cm = 3 cm

The volume of a sphere = $\frac{4}{3} \pi$(Radius of a sphere)³

Therefore, the volume of the cut sphere = $\frac{4}{3} \pi$(3)³ cm³ = $\frac{4}{3} \pi$(3 × 3 × 3) cm³

⇒ The volume of the cut sphere = 113.14 cm³

Hence, the volume of the cut sphere is equal to 113.14 cm³.