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Chain Rule, Log Differentiation & Rate of Change · Question 112 of 130

How fast is the area of the slick growing when its radius is 15 m?

Question 112

EasyOriginal 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 when its radius is 15 m?

Options for question 112

Show the answer and explanation
CorrectNot quiteAnswer C

Correct answer: C

Explanation

  1. dAdt=2πrdrdt\frac{dA}{dt} = 2\pi r\frac{dr}{dt}.

  2. 2π×15×2=60π2\pi \times 15 \times 2 = 60\pi m²/s.

Worth noting

30π30\pi is dAdr\frac{dA}{dr}, before multiplying by 2.

Concept
A rate of change through a related quantity
Typical time
90 s
Your time
—
The rule this testsRate of change of quantities
Practise this chapter →

Ten questions from Chain Rule, Log Differentiation & Rate of Change, at your own pace.

Practise this chapter →

Ten questions from Chain Rule, Log Differentiation & Rate of Change, at your own pace.