Question

The outer diameter of a spherical shell is 12 cm and its inner diameter is 8 cm,Find the volume of metal contained in the shell. Also find its outer surface area.

Answer 1

Solution:

Outer diameter of the spherical shell = 12 cm

Hence, radius = 6 cm

Inner diameter of spherical shell = 8 cm

Hence, radius = 4 cm

Now, Volume of the outer shell = $\frac{4}{3}$$\pi$$r^3$ = $\frac{4}{3}$ $\times$$\frac{22}{7}$ $6\times 6\times 6$ = 905.15 $c{m}^3$

And, Volume of the inner shell = $\frac{4}{3}$$\pi$$r^3$ = $\frac{4}{3}$ $\times$$\frac{22}{7}$ $4\times 4\times 4$ = 268.20 $c{m}^3$

Volume of metal contained in the shell = (Volume of outer) – (Volume of inner) = (905.15) -(268.20) $c{m}^3$​​​​​​​ = 636.95 $c{m}^3$​​​​​​​

∴ Outer Surface area = $\frac{4}{3}$$\pi$$r^2$​​​​​​​ = $\frac{4}{3}$ $\times$$\frac{22}{7}$ $6\times 6\times 6$ = 452.57 $c{m}^3$​​​​​​​