A piston is seated at the top of a cylindrical chamber with radius 4 cm when it

Question

A piston is seated at the top of a cylindrical chamber with radius 4 cm when it starts moving into the chamber at a constant speed of 4 cm/s(see figure). What is the rate of change of the volume of the cylinder when the piston is 11 cm from the base of the chamber? Let V, r, and h be the volume, radius, and height of a cylinder, respectively. Write an equation relating V, r, and h. (Type an exact answer, using x as needed.) Find the related rates equation. dv/dt = ()dh/dt (Type an exact answer, using x 3S needed.) When the piston is 11 cm from the base of the chamber, the volume of the cylinder is changing at a rate of about (Round to the nearest hundredth as needed.)

Explanation / Answer

V=pi r2h

a. V=16pi h

b .dV/dt=16 pi(dh/dt)

dV/dt=16pi*-11=-176picm3/sec=-552cm3/sec

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