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Chain Rule, Log Differentiation & Rate of Change · Question 122 of 130

How fast is the area of the slick growing 10 seconds after it starts?

Question 122

MediumOriginal question

An oil slick spreads as a circle whose radius grows at a steady 2 m/s, starting from a point.

How fast is the area of the slick growing 10 seconds after it starts?

Options for question 122

Show the answer and explanation
CorrectNot quiteAnswer C

Correct answer: C

Explanation

  1. After 10 s the radius is 20 m.

  2. 2π×20×2=80π2\pi \times 20 \times 2 = 80\pi m²/s.

Worth noting

40π40\pi uses r=10r = 10, the time, in place of the radius.

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