Circle Diameter Concept
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Questions and Answers

What is the formula to find the diameter of a circle using its circumference?

  • Diameter = Circumference / 2π (correct)
  • Diameter = Circumference / π
  • Diameter = Circumference + π
  • Diameter = Circumference × π

    • What is the diameter of a circle with a circumference of 10π meters?

  • 5 meters
  • 20 meters
  • 10 meters (correct)
  • 30 meters

    • 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 16π square meters?

    <p>8 meters (C)</p> Signup and view all the answers

    If the circumference of a circle is 5π inches, what is its diameter?

    <p>10 inches (D)</p> Signup and view all the answers

    What is the diameter of a circle with a circumference of 8 feet?

    <p>4 feet (A)</p> Signup and view all the answers

    If the area of a circle is 9π square inches, what is its diameter?

    <p>6 inches (D)</p> Signup and view all the answers

    What is the diameter of a circle with an area of 100π square centimeters?

    <p>20 centimeters (D)</p> Signup and view all the answers

    If the diameter of a circle is 14 centimeters, what is its circumference?

    <p>28π centimeters (D)</p> Signup and view all the answers

    What is the relationship between the circumference and diameter of a circle?

    <p>Circumference is π times the diameter (A)</p> Signup and view all the answers

    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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    Quiz Team

    Description

    Learn about the definition and properties of a circle's diameter, including its relation to the center and longest chord.

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