# volume of solid of revolutionWatch

#1
Question: the area enclosed by and y =10 is rotated about the x-axis; find the volume generated. take an element of area parallel to the x-axis of length express the typical elements of volume in terms of y by using the fact that and are the roots of

my attempt:
the graph is

when x is the subject

the interval is y =9 to y=10
the minimum point is (3,9)

Last edited by bigmansouf; 6 days ago
0
1 week ago
#2
not quite sure of your method, or the method described in the question.

By a more methodical route, we can find the required volume by

vol. cylinder (radius 10, height 2) subtract volume of revolution of y=x^2-6x+18 about x-axis

I get : 25.6pi

200pi - pi*integral[x^4 - 12x^3 +72x^2 - 108x +324] , from x=2 to x=4

geogebra vol of integration tool
0
1 week ago
#3
(Original post by bigmansouf)
Question: the area enclosed by and y =10 is rotated about the x-axis; find the volume generated. take an element of area parallel to the x-axis of length express the typical elements of volume in terms of y by using the fact that and are the roots of

my attempt:
the graph is

when x is the subject

the interval is y =9 to y=10
the minimum point is (3,9)

It looks to me that what you have tried to calculate is the volume formed by rotating the area to the left of the curve about the y axis, between y = 9 and y = 10.
begbie68 has calculated the volume mentioned in the question by starting with the volume of a disc of radius 10 and thickness 2, then subtracting the volume formed by rotating the area under the curve around the x axis. I agree with the answer 25.6(pi).
However, the question is asking you to consider a different method where the required volume is made up of a series of concentric cylindrical shells (with the x axis as the cylinder axis). Moving out from the x axis, the first cylindrical shell has radius 9 and length (x direction) 0, and the last cylindrical shell has radius 10 and length 2. You have to find a way of summing the volumes of these cylindrical shells by integration.
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