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A hemispherical tank is made up of an iron sheet 1 cmthick. If the inner radius is 1 m,then find the volume of the iron used to make the tank

Answer» Inner radius `(r_(1))=1m=100 cm`
Outer radius `(r_(2))=(100+1)cm " " (because` inner radius + thickness)
= 101 cm
Outer volume `=(2)/(3)pi(101)^(3) " " (because "volume" =(4)/(3)pi r^(3))`
Inner volume `=(2)/(3)pi(100)^(3)`
Hence, volume of the iron used to make the tank = outer volume - inner volume
`= (2)/(3)pi[(101)^(3)-(100)^(3)]`
`=(2)/(3)xx(22)/(7)(101-100)[(101)^(2)+101xx100+(100)^(2)]`
`=(2)/(3)xx(22)/(7)(10201+10100+10000)`
`=(44)/(21)(30301)=63487.80 cm^(3)`
`=(63487.80)/(100xx100xx100)m^(3)=0.063 m^(2)` (approx.)


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