JAMB Mathematics 2013 Paper

Concept: The area of a circle changes as its radius changes, so we use related rates to connect $\frac{dA}{dt}$, $\frac{dA}{dr}$, and $\frac{dr}{dt}$.Explanation:Let the radius be $r$ and the area be $A$.The area of a circle is given by $A = \pi r^2$.Differentiate $A$ with respect to $r$: $\frac{dA}{dr} = 2\pi r$.The radius increases at the rate $\frac{dr}{dt} = 0.02 \, \text{cm s}^{-1}$.Using the chain rule: $\frac{dA}{dt} = \frac{dA}{dr} \times \frac{dr}{dt}$.Substitute $r = 7 \, \text{cm}$: $\frac{dA}{dt} = 2\pi (7)(0.02)$.Using $\pi = \frac{22}{7}$, we get $\frac{dA}{dt} = 2 \times \frac{22}{7} \times 7 \times 0.02 = 0.88 \, \text{cm}^2 \text{s}^{-1}$.Therefore, the area is increasing at the rate of $0.88 \, \text{cm}^2 \text{s}^{-1}$ when the radius is $7 \, \text{cm}$.Answer: D. $0.88 \, \text{cm}^2 \text{s}^{-1}$