Discussion
The radius of a circle is increased so that its circumference is increased by 5%. Find the percentage of increase in its area.
Answer: A
If the circumference increases by 5%, the radius also increases by 5%, so the new area is 1.05 squared = 1.1025 times the old area.
The increase is 10.25%, option A. 10% and 5.5% neglect the squaring, and 25% is far too large.
Circumference is proportional to the radius, so a 5 per cent increase in the circumference means a 5 per cent increase in the radius. The area depends on the square of the radius, giving 1.05 squared = 1.1025, an increase of 10.25 per cent. The common mistake is to double the 5 per cent and answer 10.
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