Question

A solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of the cone is 2 cm and the diameter of the base is 4 cm. Determine the volume of the toy. If a right circular cylinder circumscribes the toy, find the difference of the volume of the cylinder and toy.

Answer 1

Let BPC is a hemisphere and ABC is a cone. 

Radius of hemisphere = Radius of cone

= 4/2 = 2 cm

h = Height of cone = 2 cm

= 25.12 cm³ ..........(i)

Let right circular cylinder EFGH circumscribe the given solid toy.

Radius of cylinder = 2 cm, 

Height of cylinder = 4 cm 

 Volume of right circular cylinder = πr² h 

= 3.14 × (2)² × 4 cm³ ...(ii) 

= 50.24 cm³ 

∴ Required volume = Volume of cylinder – Volume of toy 

 = 50.24 – 25.12 

 = 25.12 cm³