Radius and Diameter
In short: Radius and diameter measure the same circle in two ways: reach from the center to the rim, or stretch across the whole circle through the center, which always gives double.
7th GradeGeometry7.G.B.4
What is Radius and Diameter?
The radius and diameter of a circle describe one size from two viewpoints. Start at the center and walk to the rim, and you have walked a radius. Cross the whole circle in a straight line through the center, and you have walked a diameter.
Two radii placed back to back make a diameter, so \(d = 2r\) and \(r = \frac{d}{2}\). Within a single circle all radii match each other, and all diameters match each other. The plural of radius is radii.
How to spot it
- A circle is described by how wide it is, like a 16-inch pizza or a 30-foot pool.
- Another statement gives the reach from the center, such as the range of a lawn sprinkler.
- A circumference or area formula wants one of the two lengths but the problem hands you the other.
- A diagram labels a segment that runs through the middle of a circle.
The method
- For radius and diameter alike, decide which one you hold: center to rim is the radius, rim to rim through the center is the diameter.
- Radius to diameter: double the number.
- Diameter to radius: halve the number.
- Keep the same unit and make sure the answer is a length, not an area.
Radius and Diameter: solved example
Problem
A round backyard trampoline in Tulsa has a radius of 7.5 feet. How wide is it? A smaller one is 12 feet wide; how long is its radius?
Solution
First trampoline: \(d = 2 \times 7.5 = 15\) feet.
Smaller trampoline: \(r = \frac{12}{2} = 6\) feet. So the answers are a diameter of 15 feet and a radius of 6 feet.
Try it
Question 1
A pond is 31 meters across at its widest. What is its radius?
Show the answer
Across through the center is the diameter, so \(r = \frac{31}{2} = 15.5\) meters.
Question 2
A wall clock has a radius of 2.4 decimeters. How wide is it?
Show the answer
\(d = 2 \times 2.4 = 4.8\) decimeters.
Radius and Diameter vs. Circumference
Radius and diameter are straight lengths inside the circle, measured through the center. The circumference is the length around the outside, a curved path. It is about 3.14 times the diameter, so swapping them can throw an answer off by more than a factor of three.
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