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%
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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