What is the volume of the solid produced by revolving #f(x)=7-x, x in [0,2] #around the x-axis?

1 Answer
Steve M
Feb 27, 2017

#V = (218pi)/3 #
#\ \ \ ~~ 228.289 #

Explanation:

graph{7-x [-10.29, 9.71, -1.88, 8.12]}

#y=7-x# is a straight line; The volume of revolution is that of a large cone of radius #7# height #7# minus that of smaller cone radius #5# height #5#; Using #V_("cone") = 1/3pir^2h#, Then:

#V = 1/3pi(7)^2(7) - 1/3pi(5)^2(5) #
#\ \ \ = 1/3pi(7^3-5^3) #
#\ \ \ = 1/3pi(343-125) #

#\ \ \ = (218pi)/3 #
#\ \ \ ~~ 228.289 #

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