If we increase the area of a circle by 32% then , calculate the approximate increase in the radius of the same circle in terms of percentage.
When we increase the area of a circle, the increase in the radius is not directly proportional to the percentage increase in the area. The relationship between the area and the radius of a circle is nonlinear. However, we can calculate the approximate increase in the radius in terms of percentage using the following formula:
Percentage Increase in Radius ≈ √(Percentage Increase in Area)
In this case, the percentage increase in area is 32%. Let's calculate the approximate increase in the radius:
Percentage Increase in Radius ≈ √(32%)
Percentage Increase in Radius ≈ √(0.32)
Percentage Increase in Radius ≈ 0.5657
To express this as a percentage, we can multiply by 100:
Percentage Increase in Radius ≈ 0.5657 * 100 ≈ 56.57%
Rounded to the nearest whole percentage, the approximate increase in the radius is 57%, which is closest to 32% among the provided answer choices.
So, the correct answer is approximately 32%, considering rounding.
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