Question

1. A 2-cm thick hollow glass sphere has an external diameter of 9 cm. Find (a) its external surface area, (b) the volume of glass in the sphere. 2. A solid right circular metal cone has a base radius of 8 cm and a height of 13.5cm. It is melted and recast into a sphere. Find (a) the radius of the sphere, (b) the surface area of the sphere.

Answer 1

Answer:

Since the spherical shell is recasted into a cylinder,

Volume of the hollow sphere = Volume of the cylinder

Volume of a hollow sphere of outer Radius R and inner radius r=

3

4

π(R

3

−r

3

)

Volume of a Cylinder of Radius "R" and height "h" =πR

2

h

Hence,

3

4

×π×(8

3

−4

3

)=π×R

2

×

3

28

⇒4×(512−64)=R

2

×28

⇒R

2

=

28

4×448

=64 cm

⇒R=8 cm

Hence, diameter of the base of the cylinder =2×8=16 cm