Pi divided by the circumference of a circle equals the reciprocal of the circle's circumference, or 1/(2πR), where R is the radius. This can be simplified further depending on how the circumference is expressed.
The question "What is pi divided by circumference?" is best understood by examining the relationship between pi, circumference, and other related values like radius and diameter. The reference provides insight on these relationships.
Understanding the relationship
- The circumference (C) of a circle is given by the formula: C = 2πR where R is the radius.
- Alternatively, since the diameter (D) is twice the radius (D = 2R), the circumference can also be expressed as C = πD.
- Pi (π) is defined as the ratio of a circle's circumference to its diameter: π = C/D.
Calculating π/C
Given that C = 2πR or C= πD, dividing π by the circumference C would depend on the exact representation we use:
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Using C = 2πR:
π / C = π / (2πR) = 1 / (2R)
So, pi divided by the circumference is equal to one divided by twice the radius. -
Using C = πD:
π / C = π / (πD) = 1 / D
So, pi divided by the circumference is equal to one divided by the diameter.
Examples
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Example 1: If a circle has a radius (R) of 5, its circumference (C) would be 2 π 5 = 10π. Therefore, π / C = π / (10π) = 1/10. This aligns with 1/(2R) = 1/(2*5) = 1/10.
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Example 2: If a circle has a diameter (D) of 7, its circumference (C) would be π * 7 = 7π. Therefore, π / C = π / (7π) = 1/7. This aligns with 1/D = 1/7.
In summary, π divided by the circumference simplifies to 1/(2R) or 1/D, where R is the radius and D is the diameter of the circle, respectively.
