How do you find the volume of the solid generated when the regions bounded by the graphs of the given equations #y = sqrt (3 - x^2)#, x=0, x=1 and the x-axis are rotated about the x-axis?

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Answer 1 · 2016-07-01T11:55:50

#(8pi)/3# cubic units.

The given equation represents the circle #x^2+y^2=3

Volume =#piint y^2 dx#, from x=0 t0 x=1

#pi[3x-x^3/3], beteween x = 0 and x = 1

#=pi(3-1/3)#

#=pi(8/3)#.-

The solid generated is a slice of a hemisphere of radius sqrt 3 units,

between the base abd the parallel plane,at a distance 1 unit.i