Calculus
posted by Summer
Imagine slicing through a sphere with a plane (sheet of paper). the smaller piece produced is called a radius of the sphere. Its volume is V=(pi)h^2(3rh)/3, where r is the radius of the sphere and h is the thickness of the cap. find dr/dh for a sphere with a volume of 5pi/3m^3. evaluate the derivative when r=2m and h=1m.

Steve
we have
π/3 h^2(3rh) = 5π/3
3rh^2h^3 = 5
3h^2 dr/dh + 6rh  3h^2 = 0
h dr/dh + 2r  h = 0
dr/dh = (h2r)/h = 1  2r/h
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