Discussion
Radius of a circle is increased by 6%, determine the increase in area of the circle.
Answer: B
Area of a circle is \( \pi r^{2} \), so a 6% rise in the radius acts through the square.
\[ \frac{A'}{A} = \left(\frac{1.06r}{r}\right)^{2} = (1.06)^{2} = 1.1236 \]
\[ \text{increase} = 1.1236 - 1 = 0.1236 = 12.36\% \]
Doubling the percentage to 12% misses the square term \( \left(\tfrac{6}{100}\right)^{2} = 0.36\% \). The exact rule is \( 2x + \tfrac{x^{2}}{100} \).
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