How do you use the method of cylindrical shells to find the volume of the solid obtained by rotating

Ezekiel Yoder

Ezekiel Yoder

Answered question

2022-06-18

How do you use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by y = 1 x 4 , y=0, x=1, x=4 revolved about the x=-4?

Answer & Explanation

Rebekah Zimmerman

Rebekah Zimmerman

Beginner2022-06-19Added 32 answers

Explanation:
the formula for the shell method is a b 2 π r h d x
a and b are the x-bounds, which are x=1 and x=4, so a=1 and b=4.
r is the distance from a certain x-value in the interval [1,4] and the axis of rotation, which is x=-4. r=x-(-4)=x+4
h is the height of the cylinder at a certain x-value in the interval [1,4], which is 1 x 4 0 = 1 x 4 (because 1 x 4 is always greater than 0 and h must be positive).
plugging it all in: volume = 1 4 ( 2 π ( x + 4 ) ( 1 x 4 ) ) d x
you should get: 57 π 16

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