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JAMB 2013 · UTME · Q37

The radius of a circle is increasing at the rate of 0.02 cm s−10.02\text{ cm s}^{-1}. Find the rate at which the area is increasing when the radius of the circle is 7 cm7\text{ cm}. [Take π=227]\left[\text{Take }\pi = \frac{22}{7}\right]

Worked solution (try it first)
  1. The area is A=πr2A = \pi r^2, so dAdr=2πr\frac{dA}{dr} = 2\pi r.
  2. Chain rule: dAdt=2πr×drdt\frac{dA}{dt} = 2\pi r \times \frac{dr}{dt}
    =2×227×7×0.02= 2 \times \frac{22}{7} \times 7 \times 0.02.
  3. 2×22×0.02=0.882 \times 22 \times 0.02 = 0.88, so the area increases at 0.88 cm2s−10.88\text{ cm}^2\text{s}^{-1}, option B.

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