Solved: Spherical caps The volume of the cap of a sphere
Chapter 12, Problem 70(choose chapter or problem)
Spherical caps The volume of the cap of a sphere of radius r and thickness h is V = p 3 h213r - h2, for 0 h 2r. 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 10 h 2r2 is the rate of change of volume with respect to h the greatest?
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