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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
Solution
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
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