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Questions and Answers
A circle has a known area. Which of the following is the correct method to determine the radius?
A circle has a known area. Which of the following is the correct method to determine the radius?
- Divide the area by $2\pi$ and then square the result.
- Multiply the area by $\pi$ and take the square root of the result.
- Divide the area by $\pi$ and take the square root of the result. (correct)
- Multiply the area by $2\pi$.
If a circle's radius is doubled, what happens to its circumference?
If a circle's radius is doubled, what happens to its circumference?
- The circumference is quadrupled.
- The circumference is halved.
- The circumference is doubled. (correct)
- The circumference remains the same.
A circle has a diameter of 10 units. What is its area?
A circle has a diameter of 10 units. What is its area?
- $5\pi$ square units
- $25\pi$ square units (correct)
- $100\pi$ square units
- $10\pi$ square units
How does increasing the radius of a circle affect both its area and circumference?
How does increasing the radius of a circle affect both its area and circumference?
If two circles have the same circumference, what can be said about their areas?
If two circles have the same circumference, what can be said about their areas?
Flashcards
Area of a Circle
Area of a Circle
The amount of space enclosed within a circle, calculated by Area = πr².
Circumference of a Circle
Circumference of a Circle
The distance around the circle, calculated by Circumference = 2Ï€r.
Radius of a Circle
Radius of a Circle
The distance from the center to the circumference; half the diameter.
Diameter of a Circle
Diameter of a Circle
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Relationship Between Circle Values
Relationship Between Circle Values
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Study Notes
Area of a Circle
- The area of a circle is the amount of space enclosed within the circle's boundary.
- It is calculated using the formula: Area = πr², where 'r' represents the radius of the circle and 'π' (pi) is a mathematical constant approximately equal to 3.14159.
- A larger radius results in a larger area.
Circumference of a Circle
- The circumference of a circle is the distance around the circle's edge.
- It is calculated using the formula: Circumference = 2Ï€r, where 'r' represents the radius of the circle and 'Ï€' (pi) is a mathematical constant approximately equal to 3.14159.
- A larger radius results in a larger circumference.
Radius of a Circle
- The radius of a circle is the distance from the center of the circle to any point on its circumference.
- It is a crucial measurement for calculating both the area and circumference of a circle.
- Knowing the radius allows for the calculation of other circle properties.
- The radius is half the length of the diameter.
- A larger radius indicates a larger circle.
Relationship Between Radius, Diameter, Circumference, and Area
- The diameter of a circle is twice the length of the radius (Diameter = 2r).
- The formulas for area and circumference are directly dependent on the radius.
- Any two of these values (radius, diameter, area, circumference) can be calculated if the third is known.
- For example, if the area is known, the radius can be found by rearranging the area formula (Area = πr²).
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