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Question
Find the volume of solid generated by rotating the area bounded by x2+y2 =36 and the lines x = 0, x = 3 about X -axis.
Solution
Given curve is x2+y2=36
∴ y 2 = 36 -x2
Required volume V = `|pi int_0^3 "y"^2 "dy"|`
∴ V = `pi int_0^3 (36 - "x"^2) "dx"`
`= pi [36"x" - "x"^3/3]_0^3`
`= pi {[36(3) - 3^3/3] - 0}`
`= pi (108 - 9)`
∴ V = 99 π cubic units.
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