If the radius of a circle increases from 10 cm to 10.1 cm, then the percentage change in its area is?
- 1%
- 2%
- 3%
- 4%
Explanation
The area of the circle with radius 10 cm is A₁ = π(10)² = 100π cm².
The area of the circle with radius 10.1 cm is A₂ = π(10.1)² = 102.01π cm².
The percentage change in area is:
((A₂ - A₁) / A₁) × 100%
= ((102.01π - 100π) / 100π) × 100%
= (2.01 / 100) × 100%
= 4%
So, the percentage change in the area is 4%.
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