Spherical caps The volume of the cap of a sphere of radius r and thickness h is
a. Compute the partial derivatives Vh and Vr.
b. For a sphere of any radius, is the rate of change of volume with respect to r greater when h = 0.2r or when h = 0.8r?
c. For a sphere of any radius, for what value of h is the rate of change of volume with respect to r equal to 1?
d. For a fixed radius r, for what value of h (0 ≤ h ≤ 2r) is the rate of change of volume with respect to h the greatest?
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Calculus: Early Transcendentals (3rd Edition)
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