Finding Radius from Circumference
To find the radius of a circle from its circumference, rearrange C = 2 pi r to get r = C divided by (2 pi). For C = 14 pi cm: r = 14 pi divided by 2 pi = 7 cm. For a cone with base circumference 32 ft: r = 32 divided by 2 pi = 16/pi ft. This reverse-formula skill from enVision Mathematics, Grade 8, Chapter 8 is necessary whenever a cone or cylinder volume problem gives circumference rather than radius, a common setup in 8th grade geometry.
Key Concepts
To find the radius ($r$) of a circle given its circumference ($C$), use the formula: $$r = \frac{C}{2\pi}$$.
Common Questions
How do I find the radius of a circle given its circumference?
Rearrange C = 2 pi r to solve for r: divide both sides by 2 pi. So r = C divided by (2 pi).
A circle has circumference 20 pi meters. What is the radius?
r = 20 pi divided by 2 pi = 10 meters.
A cone base has circumference 50 cm. What is the radius?
r = 50 divided by (2 pi) = 25/pi cm, approximately 7.96 cm.
Why do I need to find the radius from circumference in 8th grade?
Volume formulas for cylinders and cones require the radius. If a problem gives circumference instead of radius or diameter, you must first calculate the radius before finding volume.
Is r = C divided by 2 pi derived from the circumference formula?
Yes. Starting from C = 2 pi r, divide both sides by 2 pi: C divided by (2 pi) = r.
When do 8th graders learn to find radius from circumference?
Chapter 8 of enVision Mathematics, Grade 8 covers this in the Surface Area and Volume unit.