Discussion
The radius of a circle is increased by 1%. Find how much % does its area increases?
Answer: D
Area varies as the square of the radius.
\[ \frac{A'}{A} = (1.01)^{2} = 1.0201 \]
\[ \text{increase} = 0.0201 = 2.01\% \]
The exact rule is \( 2x + \tfrac{x^{2}}{100} = 2 + 0.01 \). For small changes the area rises by roughly twice the percentage change in the radius, with the tiny square term as the correction.
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