A circle with radius 5cm has its radius increasing at the rate of 0.2m/s. What will be the corresponding increase in the area?

  • A 2π
  • B 5π
  • C π
  • D 4π
jamb 2002mathematics

The correct answer is A. 2π

Here is the text written in MathJax:

The area of a circle is given by the formula:

\(A = \pi r^2\),

where \A is the area and \(r\) is the radius.

If the radius is increasing at a rate of \(0.2m/s\), then the corresponding rate of increase in the area can be found by taking the derivative of the area with respect to time.

This gives us \(\frac{dA}{dt} = 2\pi r \frac{dr}{dt}\). Substituting the given values, we have \(\frac{dA}{dt} = 2\pi \cdot 5 \cdot 0.2 = 2\pi\).

So, the corresponding increase in the area is \(2\pi\) square meters per second.

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