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Calculus/Calculus (related rates)

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Expert: - 6/16/2011


Question
I have a calculus problem.  I left my notes at work so I have no idea how to do this one.  Pleaese help.
When a circular plate of metal is heated in an oven, its radius increases at a rate of 0.04cm/min. At what rate is the plate’s area increasing when the radius is 42cm?
Thank you

Answer
The area of a plate is A(t) = pi*r^2(t).
From this, we differentiate and get dA/dt = 2*pi*r(t)(dr/dt).
It is given that r(t) = 42 cm and dr/dt = 0.04 cm/min.

Putting both of these in gives 2*pi*42*0.04 = 3.36*pi, which rounds to an increase of 10.56 cm/min.

Note that the real answer is 10.55575132, and that rounds up to 10.56.
We could even round it to only 3 digits, and that would be 10.6.  

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