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Questions and Answers
What is the formula to find the diameter of a circle using its circumference?
What is the formula to find the diameter of a circle using its circumference?
- Diameter = Circumference / 2Ï€ (correct)
- Diameter = Circumference / π
- Diameter = Circumference + π
- Diameter = Circumference × π
What is the diameter of a circle with a circumference of 10Ï€ meters?
What is the diameter of a circle with a circumference of 10Ï€ meters?
- 5 meters
- 20 meters
- 10 meters (correct)
- 30 meters
What is the formula to find the diameter of a circle using its area?
What is the formula to find the diameter of a circle using its area?
- Diameter = √(A/4π)
- Diameter = √(A/π)
- Diameter = √(4πA)
- Diameter = √(4A/π) (correct)
What is the diameter of a circle with an area of 16Ï€ square meters?
What is the diameter of a circle with an area of 16Ï€ square meters?
If the circumference of a circle is 5Ï€ inches, what is its diameter?
If the circumference of a circle is 5Ï€ inches, what is its diameter?
What is the diameter of a circle with a circumference of 8 feet?
What is the diameter of a circle with a circumference of 8 feet?
If the area of a circle is 9Ï€ square inches, what is its diameter?
If the area of a circle is 9Ï€ square inches, what is its diameter?
What is the diameter of a circle with an area of 100Ï€ square centimeters?
What is the diameter of a circle with an area of 100Ï€ square centimeters?
If the diameter of a circle is 14 centimeters, what is its circumference?
If the diameter of a circle is 14 centimeters, what is its circumference?
What is the relationship between the circumference and diameter of a circle?
What is the relationship between the circumference and diameter of a circle?
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Study Notes
Diameter of a Circle
- Definition: A line that cuts a circle into two equal halves, passing through the center and ending on the opposite side.
- Property: The diameter is the longest chord of a circle.
- Infinite diameters: A circle has an infinite number of diameters, but each has the same length.
Key Features of a Circle
- Radius: A line segment starting at the center and ending at any point on the circumference. Symbol: r.
- Diameter: A line segment starting at one point on the circumference, passing through the center, and ending on the other side. Symbol: d.
- Circumference: The distance along the edge of a circle. Symbol: C.
- Area: The total space inside the circle. Symbol: A.
Radius and Diameter
- Relationship: The radius is half the length of the diameter.
- Formula: diameter = 2 × radius.
Circumference
- Definition: The length of the border of a circle.
- Formula: Circumference = π × diameter.
- Property: The circumference has a consistent ratio with the diameter.
Area of a Circle
- Definition: The 2-D space held within a circle.
- Formula: Area = π × radius².
- Property: The area has a consistent relationship with the radius and diameter.
Finding the Diameter
- From Radius: diameter = 2 × radius.
- From Circumference: diameter = Circumference ÷ π.
- From Area: diameter = √(4 × Area ÷ π).
Practice Questions
- Examples and exercises to find the diameter using radius, circumference, and area.
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