Questions and Answers
What is the formula for the area of a circle?
If the radius of a circle is doubled, how does the area change?
Which of the following describes how to calculate the area of a circle with a diameter of 10 units?
What value of π would you use if you want to estimate the area of a circle as approximately 3.14?
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What happens to the area of a circle if its radius is reduced by half?
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Study Notes
Area of a Circle
- The formula for the area of a circle is A = πr², where A is the area and r is the radius.
- Doubling the radius increases the area by a factor of four. If r is doubled to 2r, then A becomes π(2r)² = 4πr².
Calculating Area with Diameter
- To calculate the area of a circle with a diameter of 10 units, first find the radius which is 5 units (diameter / 2).
- Use the area formula: A = π(5)² = 25π square units.
Estimating with π
- For an estimation of the area of a circle as approximately 3.14, use π ≈ 3.14. This approximation simplifies calculations.
Effect of Reducing Radius
- Reducing the radius by half results in the area being reduced to one-fourth its original size. If r is halved to 0.5r, then A becomes π(0.5r)² = 0.25πr².
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Description
Test your knowledge on the area of a circle with this quiz! You will explore formulas, changes in area with radius adjustments, and methods for calculation. Perfect for students learning geometry concepts about circles.