Find the volume of a bounded region as it rotates around the Y-axis. My points are y=6; x=-2; x=2; and y=0.

Ace Duran

Ace Duran

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2022-08-16

Finding the volume of a rotating cross section.
I have to find the volume of a bounded region as it rotates around the Y-axis. My points are y = 6 ; x = 2 ; x = 2; and y = 0. What would be the steps to solving this and the solution?

Answer & Explanation

Ben Logan

Ben Logan

Beginner2022-08-17Added 13 answers

Explanation:
A rectangle formed by vertices (-2,0), (2,0), (2,6) and (-2,6) is symmetrically positioned around the y-axis, and when rotated, gives a cylinder. Simply plug in r = 2 ( 2 ) = 4 and h = 6 0 = 6 in V = π r h 2 and this gives the answer 96 π sq. units.

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