Question

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(3r-h)/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.

Answer 1

we have

π/3 h^2(3r-h) = 5π/3
3rh^2-h^3 = 5
3h^2 dr/dh + 6rh - 3h^2 = 0
h dr/dh + 2r - h = 0
dr/dh = (h-2r)/h = 1 - 2r/h
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