Question : If the diameter of a circle is increased by 8%, then its area is increased by:
Option 1: 16.64%
Option 2: 6.64%
Option 3: 16%
Option 4: 16.46%
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Correct Answer: 16.64%
Solution : Given: The diameter of a circle is increased by 8%. Let the diameter of the circle be 100 cm. Diameter after increment of 8% = 108 cm Radius before increment= 50 cm Radius after increment = 54 cm Area of circle before increment = $\pi r^2$ = $\pi$ × 50 2 = 2500$\pi$ Area of circle after increment = $\pi r^2$ = $\pi$ × 54 2 = 2916$\pi$ Percentage increased = $\frac{\text{Difference}}{\text{Area before increment}}×100$ = $\frac{2916\pi-2500\pi}{2500 \pi}×100$ = $\frac{416\pi}{2500 \pi}×100$ = 16.64% Hence, the correct answer is 16.64%.
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