Question

The outer and the inner surface areas of a spherical copper shell are 576π cm² and 324π cm² respectively. Find the volume of the material required to make the shell

Answer 1

Outer surface area of a spherical shell = 576π cm² 

4πR² = 576π

4 × R² = 576

R² =  ${\displaystyle \frac{576}{4}}$ = 144

R = ${\displaystyle \sqrt{144}}$ = 12 cm

Inner surface area of a spherical shell = 324π cm²

4πr² = 324π

4r² = 324

r² = 81

r = ${\displaystyle \sqrt{81}}$ = 9

Volume of the material required = Volume of the hollow hemisphere 

= ${\displaystyle \frac{4}{3}\pi ({\text{R}}^3-{\text{r}}^3){\text{cm}}^3}$

= ${\displaystyle \frac{4}{3}\times \frac{22}{7}({12}^3-9^3){\text{cm}}^3}$

= ${\displaystyle \frac{4}{3}\times \frac{22}{7}(1728-729){\text{cm}}^3}$

= ${\displaystyle \frac{4}{3}\times \frac{22}{7}\times 999}$

= ${\displaystyle \frac{4\times 22\times 333}{7}}$

= 4186.29 cm³ 

Volume of the material required = 4186.29 cm³