Question

The outer diameter of a spherical shell is 12 cm and it`s inner diameter is 8 cm . Find the volume of the

metal used and it`s outer surface area .​

Answer 1

Answer:

Volume of the metal used = 636.95 cm³

Outer surface area of the spherical shell = 452.57 cm²

Step-by-step explanation:

Given :

• The outer diameter of a spherical shell is 12 cm
• The inner diameter is 8 cm

To find :

the volume of the metal used and it's outer surface area.

Solution :

Radius is half the diameter.

⟼ Outer radius of the spherical shell = 12/2 = 6 cm

⟼ Inner radius of the spherical shell = 8/2 = 4 cm

Volume of the sphere = 4/3 × πr³

where r denotes radius of the sphere.

Volume of the outer shell

= 4/3 × 22/7 × 6³

= 4/3 × 22/7 × 216

≈ 905.15 cm³

Volume of the inner shell

= 4/3 × 22/7 × 4³

= 4/3 × 22/7 × 64

≈ 268.20 cm³

Volume of the metal used = Volume of the outer shell – volume of inner shell

= 905.15 – 268.20

= 636.95 cm³

Outer surface area :

Outer radius of the spherical shell = 6 cm

Outer surface area = 4πr²

= 4 × 22/7 × 6²

= 88/7 × 36

= 452.57 cm²