Question

Solve the following:
1)A solid toy is in the form of a hemisphere surmounted by a right circular cone. Height of the one is 2cm and
diameter of the base is 4cm. If a right circular cylinder circumscribes the toy, find how much more space it will
cover.​

Answer 1

Answer:

Let BPC be the hemisphere and ABC be the cone mounted on the base of the hemisphere.

Let EFGH be the right circular cylinder circumscribing.

We have

Height of the cone=OA+2cm

Diameter of the base of the cone=BC=4cm

Radius of the hemisphere =BO=

2

1

BC=

2

4

cm=2cm

OP=2cm

AP=OP+OA=2+2=4cm

Volume of the right circular cylinder

⇒πr

2

h=π×2

2

×4cm

3

=16πcm

3

volume of the solid toy ={

3

2

π×2

3

+

3

1

π×2

2

×2}cm

3

=8πcm

3

Required space = volume of the right circular cylinder - volume of the toy

=16πcm

3

−8πcm

3

=8π cm

3