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1. a) A cylindrical length of wire has a radius of 4 mm and a length...

1.

a)

A cylindrical length of wire has a radius of 4 mm and a length of 10 cm. If the length is growing at a rate of 2 cm/sec and the radius is shrinking at a rate of 1 mm/sec, what is the rate of change of the volume in cm^3 /sec at that point in time. (Be careful of units)

b) Consider the same length of wire as before (radius of 4 mm and length of 10 cm). This time we are stretching the wire at a rate of 2 cm/sec. If the total volume is not changing, what is the rate of change of the radius in mm/sec at this point in time.

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