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MTH142_Exam02 - PLEASE SIGN AND DATE Although I may have...

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PLEASE SIGN AND DATE: Although I may have discussed this exam with others, the material I have submitted here is my own. I understand what I have written and I can verbally defend what I have written. Exam 2. Part I Calculators with a Computer Algebra System may NOT be used. You will be graded on your work and communication of it. 1. (12 points; 3 pts. for each part.) The volume V of a sphere is related to the radius r by the formula V = 4 3 π r 3 . (a) Find a formula for the di ff erential dV in terms of r and dr. (b) Suppose the radius of a spherical balloon is about 4 meters. Use di ff erentials to estimate the error in the volume of the balloon if the error in the radius is about 0.2 meters. (c) A spherical balloon is being filling with air. Write out a formula for the instantaneous rate of change of the volume ( dV/dt ) of the balloon. (d) Suppose the volume of the spherical balloon is increasing at the rate of 10 cubic meters per minute. Find the instantaneous rate of change of the radius of the balloon when its radius is 4 meters.
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2. (12 pts; 2 pts. for (a) and 10 pts. for (b).)
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