A potter forms a piece of clay into a right circular cylinder. As she rolls it, the height h of the cylinder increases and the radius r decreases. Assume that no clay is lost in the process. Suppose the height of the cylinder is increasing by 0.5 centimeters per second. What is the rate at which the radius is changing when the radius is 3 centimeters and the height is 11 centimeters?

Question

Korbin Dougherty

Mathematics

30 December, 09:53

A potter forms a piece of clay into a right circular cylinder. As she rolls it, the height h of the cylinder increases and the radius r decreases. Assume that no clay is lost in the process. Suppose the height of the cylinder is increasing by 0.5 centimeters per second. What is the rate at which the radius is changing when the radius is 3 centimeters and the height is 11 centimeters?

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Answers (1)

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Suzy · Answer 1

dr/dt = - 3/44 cm/s

Step-by-step explanation:

The volume of a cylinder is given by ...

V = πr²h

Differentiating with respect to t (for constant volume), we get ...

0 = π (2rh·dr/dt + r²·dh/dt)

Solving for dr/dt, we have ...

dr/dt = dh/dt (-r² / (2rh)) = (dh/dt) (-r / (2h))

Filling in the given numbers gives ...

dr/dt = (0.5 cm/s) (-3 cm) / (2·11 cm)

dr/dt = - 3/44 cm/s