Learn about the parts of a circle and how to calculate its circumference through these examples.
Example 1: Parts of a Circle
Identify and describe the main parts of a circle.
Concept: A circle is a set of all points in a plane that are at a fixed distance from a fixed point in the plane.
Center: The fixed point inside the circle from which all points on the circle are equidistant.
Imagine a circle with a dot at its center, labeled 'O'.
Point O is the Center.
Radius (r): A line segment connecting the center of the circle to any point on the circle. All radii of the same circle are equal in length.
Imagine a circle with center O and a line segment from O to a point A on the circle.
Segment OA is a Radius.
Diameter (d): A line segment passing through the center of the circle and connecting two points on the circle. It is the longest chord of the circle. The diameter is twice the radius (d = 2r).
Imagine a circle with center O and a line segment passing through O, connecting points B and C on the circle.
Segment BC is a Diameter.
Diameter = 2 * Radius
Chord: A line segment connecting any two points on the circle. The diameter is a special type of chord that passes through the center.
Imagine a circle with a line segment connecting two points D and E on the circle, not passing through the center.
Segment DE is a Chord.
Example 2: Circumference
Explain the concept of circumference and the value of Pi (π).
Circumference (C): The distance around the circle. It is the perimeter of the circle.
Pi (π): A special mathematical constant that represents the ratio of the circumference of any circle to its diameter. It is an irrational number, approximately equal to 3.14 or 22/7.
π = Circumference / Diameter
Formula: The formula for the circumference of a circle is:
C = π * d OR C = 2 * π * r
Where d is the diameter and r is the radius.
Example 3: Calculate Circumference (given Radius)
Find the circumference of a circle with a radius of 7 cm. (Use π = 22/7)
Step 1: Identify the given value: Radius (r) = 7 cm. The value of π to use is 22/7.
Step 2: Use the formula for circumference involving radius:
C = 2 * π * r
Step 3: Substitute the values into the formula:
C = 2 * (22/7) * 7
Step 4: Calculate the circumference.
C = 2 * 22 * (7/7)
C = 2 * 22 * 1
C = 44
Result: The circumference of the circle is 44 cm.
Example 4: Calculate Diameter (given Circumference)
The circumference of a circle is 66 cm. Find its diameter. (Use π = 22/7)
Step 1: Identify the given value: Circumference (C) = 66 cm. The value of π to use is 22/7.
Step 2: Use the formula for circumference involving diameter:
C = π * d
Step 3: Substitute the values into the formula:
66 = (22/7) * d
Step 4: Solve for the diameter (d). Multiply both sides by 7/22 (the reciprocal of 22/7).
d = 66 * (7/22)
Step 5: Calculate the diameter.
d = (66 / 22) * 7
d = 3 * 7
d = 21
Result: The diameter of the circle is 21 cm.
Practice Mode
Enter a problem to calculate the circumference or diameter of a circle.
Note: Enter problems like "circumference if radius is 7" or "diameter if circumference is 66". Use Pi as 22/7 for these calculations.
Related Concepts
Explore these related mathematical concepts to deepen your understanding of circles.
Center
The fixed point inside the circle.
Radius
Distance from the center to any point on the circle.
Diameter
A chord passing through the center (twice the radius).
Chord
A line segment connecting two points on the circle.
Arc
A part of the circumference of a circle.
Sector
A region bounded by two radii and an arc.
Segment
A region bounded by a chord and an arc.
Pi (π)
The ratio of a circle's circumference to its diameter (approx. 22/7 or 3.14).