(Q3)A solid toy is in the form of a right circular cylinder with hemispherical shape at one end and a cone at the other end. Their common diameter is 4.2 cm and the height of the cylindrical and conical portions are 12 cm and 7 cm respectively. Find the volume of the solid toy.

7 cm12 cm2.1 cmh1h2r

Let the height of the conical portion h1 = 7 cm

The height of cylindrical portion h2 = 12 cm

Radius (r) =
4.2
2
 = 2.1 =
21
10
 cm

Volume of the cone = Volume of the cone + Volume of the cylinder + Volume of the hemisphere.

=
1
3
 πr2h1 + πr2h2 +
2
3
 πr3
= πr2 [
1
3
 h1 + h2 +
2
3
 r]
=
22
7
 × (
)2 × [
1
3
 × + +
2
3
 ×
]
=
22
7
 ×
× [
3
 +
1
 +
5
 ]
=
22
7
 ×
× [
+ +
15
 ]
=
22
7
 ×
×
15
 =
= cm3