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 =  `576/4` = 144

R = `sqrt(144)` = 12 cm

Inner surface area of a spherical shell = 324π cm²

4πr² = 324π

4r² = 324

r² = 81

r = `sqrt(81)` = 9

Volume of the material required = Volume of the hollow hemisphere 

= `4/3 pi("R"^3 - "r"^3) "cm"^3`

= `4/3xx 22/7 (12^3 - 9^3) "cm"^3`

= `4/3 xx 22/7 (1728 - 729) "cm"^3`

= `4/3 xx 22/7 xx 999`

= `(4 xx 22 xx 333)/7`

= 4186.29 cm³ 

Volume of the material required = 4186.29 cm³