Volumes by Disk and Washer Methods

AP Calculus AB· difficulty 3/5

Rotate y=xy = x, 0xH0 \le x \le H about the xx-axis. Volume:

  • A

    πH3/2\pi H^3/2

  • B

    πH2/3\pi H^2/3

  • C

    πH3\pi H^3

  • D

    πH3/3\pi H^3/3

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Explanation

V=π0Hx2dx=πH3/3V = \pi\int_0^H x^2\,dx = \pi H^3/3.

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