Verify the volume of a sphere of radius R via disks: V = \pi\int{-R}^{R} (R^2 - y^2)\,dy =

\tfrac{4}{3}\pi R^3 \pi[R^2 y - y^3/3]{-R}^{R} = \pi(2R^3 - 2R^3/3) = (4/3)\pi R^3.

Volumes by Disk and Washer Methods

AP Calculus AB· difficulty 3/5

R

Explanation

\pi[R^2 y - y^3/3]_{-R}^{R} = \pi(2R^3 - 2R^3/3) = (4/3)\pi R^3

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