Questions and Answers
What is the formula to find the diameter of a circle using its circumference?
What is the diameter of a circle with a circumference of 10π meters?
What is the formula to find the diameter of a circle using its area?
What is the diameter of a circle with an area of 16π square meters?
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If the circumference of a circle is 5π inches, what is its diameter?
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What is the diameter of a circle with a circumference of 8 feet?
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If the area of a circle is 9π square inches, what is its diameter?
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What is the diameter of a circle with an area of 100π square centimeters?
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If the diameter of a circle is 14 centimeters, what is its circumference?
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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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Description
Learn about the definition and properties of a circle's diameter, including its relation to the center and longest chord.
