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NECO 2022 · Paper 1 · Q59

When a stone is dropped into water, the radius of a circular wave is increasing at the rate of 0.2 m s−10.2\text{ m s}^{-1}. Find the rate at which the area is increasing when the radius is 0.07 m.

Worked solution (try it first)
  1. The area is A=πr2A = \pi r^2, so dAdr=2πr\dfrac{dA}{dr} = 2\pi r.
  2. Chain rule: dAdt=dAdr×drdt\dfrac{dA}{dt} = \dfrac{dA}{dr} \times \dfrac{dr}{dt}
    =2πr×0.2= 2\pi r \times 0.2.
  3. Put in r=0.07r = 0.07: 2×227×0.07×0.2=0.088 m2s−12 \times \frac{22}{7} \times 0.07 \times 0.2 = 0.088\text{ m}^2\text{s}^{-1}, option D.

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