Circumference from Radius
The circumference of a circle from the radius uses the formula C = 2 x pi x r, where pi is approximately 3.14. In Grade 6 Saxon Math Course 1 (Chapter 5: Number and Operations), students derive this formula from C = pi x d by substituting d = 2r. For a circle with radius 5 cm: C = 2 x 3.14 x 5 = 31.4 cm. Students use this formula when the radius is given directly, avoiding the intermediate step of doubling to find the diameter. They also solve in reverse: given circumference, divide by 2 x pi to find the radius.
Key Concepts
Property Since a diameter is equal to two radii (2r), the formula for circumference using the radius (r) is $C = 2\pi r$.
Examples A circle with a 2 inch radius has a circumference of $C \approx 2 \cdot 3.14 \cdot 2 \text{ in.} = 12.56 \text{ in.}$ A circle with a 3 cm radius has a circumference of $C \approx 2 \cdot 3.14 \cdot 3 \text{ cm} = 18.84 \text{ cm.}$ A circle with a 5 inch radius has a circumference of $C \approx 2 \cdot 3.14 \cdot 5 \text{ in.} = 31.4 \text{ in.}$.
Explanation Only know the radius? No problem! The radius is the distance from the center to the edge, so just double it to get the full diameter. The formula $C = 2\pi r$ does this for you by combining the doubling and the multiplication with $\pi$ into one smooth move. It's like getting a two for one deal for your calculation!
Common Questions
What is the circumference formula using radius?
C = 2 x pi x r, where pi is approximately 3.14 and r is the radius.
Find the circumference of a circle with radius 7 cm.
C = 2 x 3.14 x 7 = 43.96 cm.
How is C = 2 x pi x r derived from C = pi x d?
Since diameter d = 2r, substituting into C = pi x d gives C = pi x 2r = 2 x pi x r.
When should you use C = 2 x pi x r versus C = pi x d?
Use C = 2 x pi x r when you are given the radius. Use C = pi x d when you are given the diameter.
A circle has circumference 62.8 cm. What is its radius? (Use pi = 3.14)
r = C / (2 x pi) = 62.8 / (2 x 3.14) = 62.8 / 6.28 = 10 cm.