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A

Anonymous

Feb 20, 2025

Calculus,Sketch a washer and Find the Volume of the Solid generatedBy Revolving the region bounded by y=2x^2, y=0, and x=2 around the y-axis?

Title: Calculating Volume Using the Washer Method

Body: Can someone please help me with a calculus problem? I need to sketch the washer that represents the solid generated by revolving the region bounded by the curves (y = 2x^2), (y = 0), and the vertical line (x = 2) around the y-axis. Once I have the sketch, I would also like assistance in finding the volume of the solid generated by this revolution. Thank you!

1 Answers

A
Anonymous

Dec 24, 2024

Shell method:

radius = x

height = 2x^2

Volume = 2 pi ∫ x (2x^2) dx , x=0 to 2

= 4 pi ∫ x^3 dx , x=0 to 2

= 16 pi

Washer:

Volume = pi ∫ (2^2 – (sqrt(y/2))^2 ) dy, y=0 to 8

= pi ∫ (2^2 – y/2 ) dy, y=0 to 8

= 16pi

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