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Chain Rule, Log Differentiation & Rate of Change · Question 105 of 130

Question 105

EasyOriginal question

A stone dropped into a pond sends out a circular ripple whose radius grows at 5 cm/s. How fast is the area inside the ripple growing when the radius is 8 cm?

Options for question 105

Show the answer and explanation
CorrectNot quiteAnswer D

Correct answer: D

Explanation

  1. A=πr2A = \pi r^{2}, so dAdt=2πrdrdt\frac{dA}{dt} = 2\pi r\frac{dr}{dt}.

  2. 2π×8×5=80π2\pi \times 8 \times 5 = 80\pi cm²/s.

Worth noting

16π16\pi is dAdr\frac{dA}{dr} at r=8r = 8, before multiplying by drdt=5\frac{dr}{dt} = 5.

Concept
A rate of change through a related quantity
Typical time
60 s
Your time
—
The rule this testsRate of change of quantities
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