If a region is bounded by #y = sqrt(x) + 3#, #y=5#, and the y=axis and it is revolved around the y = 7, how do you find the volume?

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Answer 1 · 2016-11-18T12:12:23

The volume is #=120pi#

The volume of a small slice,

#dV=pi(7-(sqrtx+3))^2dx#

Therefore,

#V=int_0^4pi(7-(sqrtx+3))^2dx#

#V=piint_0^4 (49-(x+6sqrtx+9))dx#

#=piint_0^4 (49-x-6sqrtx-9)dx#

#=pi[40x-x^2/2-6x^(3/2)/(3/2)]_0^4#

#=pi(160-8-32)=120pi#

graph{(y-(sqrtx+3))(y-5)(y-7)=0 [-5.335, 10.465, 2.226, 10.126]}