(Q5)The diameter of the internal and external surfaces of a hollow hemisperical shell are 6 cm and 10 cm, respectively.It is melted and recast into a solid cylinder of diameter 14cm.Find the height of the cylinder.

.6 cm10 cm hrr
Outer radius of hollow hemispherical shell R =
10
2
 = 5 cm
Internal radius of hollow hemispherical shell(r) =
6
2
 = 3 cm.

Volume of hollow hemispherical shell = External Volume - Internal Volume

=
2
3
 πR3 -
2
3
 πr3
=
2
3
 π(R3 - r3)
=
2
3
 π( 3 - 3)
=
2
3
 π( - )
=
2
3
 π × cm3
=
π
3
 cm3   .....(1)

Since, this hollow hemispherical shell is melted and recast into a cylinder. So, their volumes must be equal

Diameter of cylinder = 14 cm (given)

So, radius of cylinder = 7 cm

Let the height of cylinder = h

∴ Volume of cylinder = πr2h

= π × × × h cm3

= πh cm3   .....(2)

According to given condition,

Volume of hollow hemispherical shell = Volume of solid cylinder

3
 π = πh   [From equation (1) and (2)]
⇒ h =
3 ×
=
cm

Hence, height of the cylinder = cm