Question

A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 60 cm/s. Find the rate at which the area within the circle is increasing after each of the following.
after 2s : cm2/s
after 5s : cm2/s
after 6s : cm2/s

Answer 1

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Answer:

• 2s: 45,239 cm²/s
• 5s: 113,097 cm²/s
• 6s: 135,717 cm²/s

Step-by-step explanation:

The radius is a function of time:

  r(t) = 60t . . . . . radius in cm; time in s

Then the area of the circle is ...

  A = πr² = π(60t)² = 3600πt²

The rate of change of area is the derivative of this:

  A' = 2·3600πt = 7200πt

The rates of change of interest are ...

  after 2s: 45,239 cm²/s

  after 5s: 113,097 cm²/s

  after 6s: 135,717 cm²/s