Question : If the radius of a circle is increased by 5%, then the increase in its area is:
Option 1: 10.25%
Option 2: 10%
Option 3: 5.75%
Option 4: 5%
Correct Answer: 10.25%
Solution :
The area of a circle with $r$ as the radius $=\pi r^2$
The radius is increased by $5\%$, the new radius becomes $1.05r$.
The new area of the circle $=\pi (1.05r)^2 = 1.1025 \pi r^2$
The increase in the area $=1.1025 \pi r^2 - \pi r^2 = 0.1025 \pi r^2$
The percentage increase in the area $=\frac{0.1025 \pi r^2}{\pi r^2} \times 100 = 10.25\%$
Hence, the correct answer is 10.25%.
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