Use polar coordinates to find the volume of the given solid.

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Question

Use polar coordinates to find the volume of the given solid.

Use polar coordinates to find the volume of the given solid.

Inside both the cylinder x2 + y2 = 6 and the ellipsoid 4x2 + 4y2 + z2 = 64.

I know how to solve most of it, but could someone rework it and show your steps so that I can make sure I am doing it correctly.

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Answer 1

Answer #1

x=√6 cosθ y=√6 sinθ

z²=64-4x²-4y²

=>z²=64-4*6 = 40

=>z²-40=0

z varies from -8 to 8

∫(z²-40)dz = (z³/3 - 40z) from -8 to 8

= 512-(-512)/3 - 40(8--8)

= 1024/3 - 640

= (1024-1920)/3

= 896/3 = 298.67

hence volume of the given solid is 298.67cubic units

answered by: oso

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Answer 2

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