Find the rate of change of volume of a cone w.r.t. its radius, when the height is kept constant.
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Answer:
rate of change of volume = (2/3) π rh
Step-by-step explanation:
Volume of a cone = (1/3) π r²h
where r = radius of cone
& h = height of cone
& rest are constant
Now we need to find rate of change of Volume with respect to radius when the height is kept at constant
=> V = (1/3) π h * r²
where only r is variable , rest is constant
dV/dr = (1/3) π h (2r)
=> dV/dr = (2/3) π rh
rate of change of volume = (2/3) π rh
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