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Chain Rule, Log Differentiation & Rate of Change · Question 113 of 130

How fast is the circumference of the slick growing?

Question 113

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 circumference of the slick growing?

Options for question 113

Show the answer and explanation
CorrectNot quiteAnswer D

Correct answer: D

Explanation

  1. C=2πrC = 2\pi r, so dCdt=2πdrdt\frac{dC}{dt} = 2\pi\frac{dr}{dt}.

  2. 2π×2=4π2\pi \times 2 = 4\pi m/s, the same at every moment.

Worth noting

2π2\pi is dCdr\frac{dC}{dr}; the radius changes at 2 m/s.

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.