(Q10).A metallic sphere of radius 4.2 cm. is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder.

Answer:

Given, sphere converted into cylinder.

Hence volume of the sphere = volume of the cylinder.

Sphere:

Radius, r = 4.2 cm

Volume V =
4
3
 πr3
=
×
× × ×

= × × × ×

=

Cylinder:

Radius, r = 6 cm

Height h = h say

Volume = πr2h

=
× × ×
=
×
=
Hence,
=
h =
×
 = cm

!! π can be cancelled on both sides i.e., sphere = cylinder

4
3
 πr13=πr22h
4
3
 r13=r22h
∴ h =
4r1
3r2
 =
× × ×
× ×

= × ×

= cm.