(Q3).A solid toy is in the form of a right circular cylinder with a hemispherical shape at one end and a cone at the other end. Their common diameter is 4.2 cm and height of the cylindrical and conical portion are 12 cm and 7 cm respectively. Find the volume of the solid toy. [π =
22
7
 ]

12 cm4.2 cm7 cm

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

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

Hemisphere:

Radius =
d
2
 =
= cm
V =
2
3
 πr3 =
×
×××

=cm3

Cylinder:

Radius, r =
d
2
 =
= cm

height, h = 12 cm

V = πr2h

=
×××

= cm3

Cone: Radius, r =
d
2
 =
= cm

Height, h = 7 cm

Volume =
1
3
 πr2h
=
×
× × ×

= cm3

∴ Total volume = + + = cm3.