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Circumference to Diameter
Circumference to diameter of a circle is a ratio used to define the standard definition of Pi (π). The circumference is its boundary or the length of a circle. Whereas, the diameter is a straight line joining a point from one end of the circle to a point on the other end, passing through the center. Let us learn more about circumference to diameter, the formulas, and solve a few examples.
|1.||Circumference to Diameter Definition|
|2.||Circumference to Diameter Formula|
|3.||Method To Calculate Circumference From Diameter|
|4.||Difference Between Circumference and Diameter|
|5.||FAQs on Circumference to Diameter|
Circumference to Diameter Definition
The circumference to diameter is the ratio where it defines π since circumference is related to the diameter. We know that the circle is a collection of points that are equidistant from the center point O. If the diameter 'd' is known, you can easily find the circumference C using the relation: C = πd. So, when the circumference C is placed in a ratio with the diameter d, the answer we get is π. And the standard definition of π is the ratio of circumference and diameter of a circle.
Circumference to Diameter Formula
Circumference of a circle can be found using the radius or the diameter. A radius is a line segment joining the center to the boundary of a circle i.e. the length is half of the diameter. To calculate these three measurements of a circle, different formulas are used. Let us see the formulas:
|Circumference of circle with radius||C = 2πr|
|Diameter of a circle with radius||D = 2r|
|Circumference of circle with diameter||C = πd|
- C = Circumference
- r = Radius
- d = Diameter
- π = 22/7 or 3.142 approx
Method To Calculate Circumference From Diameter
To calculate the circumference of a circular shape when the diameter is given we need to use the formula, C = πd. There are two simple steps required here,
- Step 1: The diameter of the shape is mentioned. If not, we need to calculate it with the help of the radius and use any of the above formulas.
- Step 2: Multiply π with the diameter to get the final result.
Example: Jason wants to paint the outer boundary of a circular swimming pool. He knows that the diameter of the pool is 50 feet. To calculate the amount of paint required he needs the circumference of the pool. Let's help him to calculate it.
Solution: Given, Diameter (d) = 50 feet.
Use the formula for circumference C = πd = 50 × π = 50 × 3.142 = 157.1 approx.
Therefore, the circumference of the pool is approximately 157.1 feet.
Difference Between Circumference and Diameter
Circumference and diameter are considered as the two important measurements for a circle. They share a relationship in the form of an equation i.e. C = πd. Look at the table below to understand circumference vs diameter.
|It is the length of one complete lap around the circle.||It is the length of the line segment that cuts a circle in half.|
|It is considered as the outer measurement.||It is considered as the inner measurement.|
|It is considered the perimeter of a circle.||It is the length of two points on the circumference of the circle.|
- π (Pi) is a mathematical constant that is the ratio of the circumference of a circle to its diameter. It is approximated to π = 22/7 or 3.14.
- We can find the circumference of a circle using the radius or diameter.
- The circumference C and diameter d of a circle are related as C= πd
Here is the list of a few topics related to circumference to diameter.
Circumference to Diameter Examples
Example 1: Michael has a circular park of diameter 21 feet in front of his house. He wants to fence the park. He wants to know the length of the rope required for fencing. Can you help him?
The diameter of the park is d= 21 feet.
To find the length of the rope, we will need the circumference of the park.
Let the circumference be C feet.
C = πd
C = (22/7) × 21
C = 66
Therefore, Michael will need a rope with length of 66 feet.
Example 2: John is repairing a pipe in his bathroom. The diameter of the pipe is 2 inches. Can you determine the length of the tape to wrap around the pipe?
The diameter of the pipe is d = 2 inches
To find the length of the tape, we will determine the circumference of the pipe.
Let the circumference be C inches.
C = πd
C = (22/7) × 2
C = 6.285
Therefore, the required length of the tape is 6.285 inches.
Example 3: The circumference of a wheel is 440 cm. Find its radius and diameter.
The Circumference of the wheel = 440 cm
Circumference of a circle formula = 2πr
Let us substitute the known values to find the radius first.
440 = 2πr
440 = 2 × (22/7) × r
radius = 70 cm
Diameter = 2 × radius
Diameter = 2 × 70
Therefore, the radius is 70 cm, and the diameter is 140 cm.
Practice Questions on Circumference to Diameter
FAQs on Circumference to Diameter
How Do You Convert Circumference to Diameter?
The formula for calculating the circumference with diameter is C = πd. Hence, to determine the diameter from the circumference we divide the value of the circumference by π, where π = 22/7 or 3.142.
What is the Circumference of a 12-foot Diameter Circle?
The circumference of a circle with a diameter of 12 feet is calculated as:
C = πd = 22/7×12 = 37.714feet.
What is the Circumference of a 3-foot Diameter Circle?
The circumference of a circle with a diameter of 3 feet is calculated as:
C = πd =22/7×3 = 9.428feet.
Is Diameter Half of a Circle?
No, the diameter is not half of a circle. It is twice the radius of a circle.
How Many Diameter are in a Circumference?
Circumference is considered to be little more than three times the diameter of a circle. Hence, we can say that it is a little more than three times to the value of π.
What is the Circumference to Diameter Formula?
The circumference to diameter formula is C = πd, where C is the circumference, d = diameter, π = 22/7 or 3.142.