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Percentage Change in Area of Circle is the increase or decrease in the area of the circle compared to its original area, expressed as a percentage. It quantifies how much the area has changed due to a change in the radius.
The calculator uses the formula:
Where:
Explanation: Since the area of a circle is proportional to the square of its radius (A = πr²), a percentage change in radius results in a squared percentage change in area when expressed in relative terms.
Details: Calculating percentage change in area is important in various fields including engineering, architecture, and physics where circular objects are involved. It helps in understanding how changes in dimensions affect the overall area coverage.
Tips: Enter the percentage change in radius (positive for increase, negative for decrease). The calculator will compute the corresponding percentage change in area.
Q1: Why is the area change squared compared to radius change?
A: Because area is proportional to the square of the radius (A = πr²), so any change in radius affects the area by the square of that change factor.
Q2: What does a negative percentage change indicate?
A: A negative percentage change indicates a decrease in either the radius or the area, depending on which value is being referenced.
Q3: How does a 10% increase in radius affect the area?
A: A 10% increase in radius results in a 21% increase in area ((1.1² - 1) × 100 = 21%).
Q4: Can this formula be used for percentage decreases?
A: Yes, the formula works for both increases and decreases in radius. For a decrease, use a negative percentage value.
Q5: Is this relationship specific to circles?
A: The squared relationship between linear dimension changes and area changes applies to all two-dimensional shapes, though the exact formula may vary for different shapes.