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Questions and Answers
What is the formula for the area of a circle?
What is the formula for the area of a circle?
- πr^2 (correct)
- πd
- r^2
- 2Ï€r
If the radius of a circle is doubled, how does the area change?
If the radius of a circle is doubled, how does the area change?
- It remains the same.
- It increases by a factor of eight.
- It doubles.
- It quadruples. (correct)
Which of the following describes how to calculate the area of a circle with a diameter of 10 units?
Which of the following describes how to calculate the area of a circle with a diameter of 10 units?
- Use the formula $5^2$. (correct)
- Use the formula $2.5^2$.
- Use the formula $10^2$.
- Use the formula $r^2$ where $r$ is 10.
What value of π would you use if you want to estimate the area of a circle as approximately 3.14?
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?
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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