Instantaneous rate of change of a sphere

AI Thread Summary
To find the instantaneous rate of change of the volume V of a sphere with respect to its radius r, the derivative of the volume formula V=4/3π(r^3) must be calculated. The derivative is dV/dr = 4πr^2. Evaluating this at r=5 micrometers gives a non-zero result, specifically 100π micrometers squared. The initial confusion stemmed from misunderstanding the nature of the derivative, which is not zero. Understanding the correct application of calculus is crucial for solving such problems.
ivysmerlin
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Homework Statement


Find the instantaneous rate of change of V with respect to r when r=5 micrometers


Homework Equations



V=4/3pi(r^3)

The Attempt at a Solution



would you just take the derivative? and if so, wouldn't it just be zero, because it comes out to be a real number, right? but that doesn't seem right...
 
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What is the derivative of V=4/3pi(r^3)? Now what would the value be at r=5micrometers? Not zero.
 
ooh, I am an idiot, thanks
 

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