Question

The radius r of a circle is increasing at a rate of 4 centimeters per minute.
(a) Find the rate of change of the area when r = 6 centimeters.
(b) Find the rate of change of the area when r = 36 centimeters.

Answer 1

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Answer:

  (a) 48π cm²/min ≈ 150.80 cm²/min

  (b) 288π cm²/min ≈ 904.78 cm²/min

Step-by-step explanation:

The area of a circle of radius r is given by the formula ...

  A = πr²

Then the rate of change of area is ...

  A' = 2πr·r'

For the given rate of change of radius, this will be ...

  A' = 2πr·(4 cm/min) = 8πr cm/min

(a)

When r = 6 cm, the rate of change of area is ...

  A' = 8π(6 cm) cm/min = 48π cm²/min ≈ 150.80 cm²/min

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(b)

When r = 36 cm, the rate is ...

  A' = 8π(36 cm) cm/min = 288π cm²/min ≈ 904.78 cm²/min