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 / 2Ï€ (correct)
  • Diameter = Circumference / Ï€
  • Diameter = Circumference + Ï€
  • Diameter = Circumference × Ï€

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?

  • Diameter = √(A/4Ï€)
  • Diameter = √(A/Ï€)
  • Diameter = √(4Ï€A)
  • Diameter = √(4A/Ï€) (correct)

What is the diameter of a circle with an area of 16Ï€ square meters?

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

If the circumference of a circle is 5Ï€ 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 9Ï€ 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 100Ï€ 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>28Ï€ 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

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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 = Ï€ × 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 = Ï€ × 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 ÷ Ï€.
  • From Area: diameter = √(4 × Area ÷ Ï€).

Practice Questions

  • Examples and exercises to find the diameter using radius, circumference, and area.

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