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.
(Class 10 Maths Sample Question Paper)

Answer 1

FIGURE IS IN THE ATTACHMENT

SOLUTION:
Given :

Diameter of the base= 4cm
Height of the cone= 2cm

Let BPC is a hemisphere and ABC is a cone.
Radius of hemisphere = Radius of cone
= 4/2 = 2 cm

Volume of toy = volume of hemisphere + volume of cone

Volume of toy = ⅔(πr³) + ⅓(πr²h)
= ⅔(3.14 × 2³) + ⅓(3.14 × 2²× 2)
= ⅔(3.14 × 8) + ⅓(3.14 × 4× 2)
= ⅔(3.14 × 8) + ⅓(3.14 × 8)
=( 3.14 × 8 )(⅔+⅓)
=(25.12) (3/3)
= 25.12 × 1
= 25.12 cm³…………..(1)

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 = πr²h
= 3.14 × 2² × 4
= 3 .14 × 4 × 4
= 3.14 × 16
= 50.24 cm³

Required volume=  volume of cylinder -  volume of toy
Required volume = 50.24 - 25.12 = 25.12 cm³

Hence, the difference of the volume of the cylinder and toy is 25.12 cm³.

HOPE THIS WILL HELP YOU....

Answer 2

volume of toy is 25.142871. &. and it is the same answer for the difference in volume of toy and cylinder