related rate question-
A potter places a cylindrical clump of clay on her wheel. Before she begins to shape it, it has a radius of 10 inches and a height of 4 inches. Assuming that no clay is lost in the shaping process and that the lump stays cylindrical throughout the process, how fast is the height of the lump changing when the radius is 4 inches and changing at 1 inch per minute? (Does the volume stay constant?)

Question

related rate question-
A potter places a cylindrical clump of clay on her wheel.  Before she begins to shape it, it has a radius of 10 inches and a height of 4 inches.  Assuming that no clay is lost in the shaping process and that the lump stays cylindrical throughout the process, how fast is the height of the lump changing when the radius is 4 inches and changing at 1 inch per minute?  (Does the volume stay constant?)

anonymous · Answer

V is constant because no clay is lost...

anonymous · Answer

V= pir^2*h
dV/dt = 0 = pi (2r*r'h + r^2*h')

anonymous · Answer

solve for h'  ...  plug in r and r'   find h from  V= pi*(10)^2*4 = pi*(4^2)*h

anonymous · Answer

i thought you were supposed to use implicit differentiation to take the derivative of that

anonymous · Answer

so wouldn't it be

anonymous · Answer

yep.

anonymous · Answer

r and h are both functions of time ...

anonymous · Answer

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