If the circumference of a circle is 16π, what is the radius?
Understand the Problem
The question is asking to find the radius of a circle given its circumference. The circumference is provided in the form of an expression (16π), and the formula for circumference (C = 2πr) is given. We will use this information to solve for the radius (r).
Answer
The radius is $r = 8$.
Answer for screen readers
The radius of the circle is $r = 8$.
Steps to Solve
- Set up the formula for circumference
The formula for the circumference of a circle is given by
$$ C = 2\pi r $$
where $C$ is the circumference and $r$ is the radius.
- Substitute the given circumference
In this problem, the circumference $C$ is provided as $16\pi$. We can substitute this into our formula:
$$ 16\pi = 2\pi r $$
- Isolate the radius
To solve for $r$, divide both sides by $2\pi$:
$$ r = \frac{16\pi}{2\pi} $$
- Simplify the equation
Now simplify the right side. The $\pi$ cancels out:
$$ r = \frac{16}{2} $$
- Calculate the final value for the radius
Perform the division:
$$ r = 8 $$
The radius of the circle is $r = 8$.
More Information
The radius is a key measurement in circles, and it represents the distance from the center of the circle to any point on its circumference. Knowing the radius allows you to calculate other properties of the circle, such as area and diameter.
Tips
- Forgetting to cancel $\pi$ when simplifying.
- Misplacing the terms when isolating $r$; ensure the right operations are performed.
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