2. Acylindrical tank with radius 5m is being filled with water at a rate of 3 m'/min. How fast is the height of the water increasing? s toward first base sing at the momen a) Draw a picture and label it appropriately. b) Write an equation relating volume of the cylinder and the radius. (Note: is there a value in the problem that is NOT changing with respect to time? If so, we can put that in the equation BEFORE we differentiate.) c) Differentiate with respect to time. d) Use this to answer the question stated in the problem. e) Does the sign of your answer make sense? i.e., do we expect to see a positive rate of change or a negative rate of change?

2. Acylindrical tank with radius 5m is being filled with water at a rate of 3 m'/min. How fast is the height of the water increasing? s toward first base sing at the momen a) Draw a picture and label it appropriately. b) Write an equation relating volume of the cylinder and the radius. (Note: is there a value in the problem that is NOT changing with respect to time? If so, we can put that in the equation BEFORE we differentiate.) c) Differentiate with respect to time. d) Use this to answer the question stated in the problem. e) Does the sign of your answer make sense? i.e., do we expect to see a positive rate of change or a negative rate of change?

Mathematics For Machine Technology

8th Edition

ISBN:9781337798310

Author:Peterson, John.

Publisher:Peterson, John.

Chapter65: Achievement Review—section Six

Section: Chapter Questions

Problem 57AR: Solve these prism and cylinder exercises. Where necessary, round the answers to 2 decimal places...

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2. A cylindrical tank with radius 5 m is being filled with water at a rate of 3 m/min. How fast is the
height of the water increasing?
s toward first base
sing at the moment
a) Draw a picture and label it appropriately.
b) Write an equation relating volume of the cylinder and the radius. (Note: is there a value in the
problem that is NOT changing with respect to time? If so, we can put that in the equation
BEFORE we differentiate.)
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c) Differentiate with respect to time.
d) Use this to answer the question stated in the problem.
e) Does the sign of your answer make sense? i.e., do we expect to see a positive rate of change or a
negative rate of change?
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