Calculate Circle Radius: Using Circumference = 14 and C = 2πr

Q: Why is my answer 7/π instead of a decimal?

Leaving the answer as $ \frac{7}{\pi} $ is the exact form! Converting to decimal (≈ 2.23) gives an approximation. In mathematics, exact answers are often preferred over rounded decimals.

Q: How do I remember the circumference formula?

Think of it as "2 times π times radius". The 2 comes from the fact that circumference is the distance around the circle, which relates to the diameter (2r).

Q: What if I got 14π as my answer?

This means you multiplied instead of dividing! Remember: we're given the circumference (14) and need to find the radius, so we must divide by 2π to isolate r.

Q: Can I use 3.14 instead of π?

You can, but your answer will be an approximation. Using π keeps the answer exact. If asked for a decimal approximation, then substitute π ≈ 3.14159.

Q: Why do we divide both sides by 2π?

We need to isolate the variable r. Since r is multiplied by 2π in the equation 14 = 2πr, we divide both sides by 2π to get r by itself on one side.

Circle Circumference with Radius Isolation

The circumference of a circle is 14.

How long is the circle's radius?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 First, let's find the radius of the circle.

00:08 We'll use the formula for the circumference of a circle, which is two times pi times R.

00:17 Now, we'll take the given circumference, plug it into the formula, and solve for the radius.

00:23 Let's focus on isolating R, the radius.

00:28 And there we go! That's how you find the radius of a circle. Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The circumference of a circle is 14.

How long is the circle's radius?

Step-by-step solution

We begin by using the formula:

$P=2\pi r$

We then insert the given data into the formula:

$14=2\times\pi\times r$

Lastly we divide Pi by 2:

$\frac{14}{2\pi}=\frac{2\pi r}{2\pi}$

$\frac{7}{\pi}=r$

Final Answer

$\frac{7}{\pi}$

Key Points to Remember

Essential concepts to master this topic

Formula: Circumference equals 2π times radius (C = 2πr)
Technique: Divide both sides by 2π: 14/(2π) = 7/π
Check: Multiply radius by 2π: (7/π) × 2π = 14 ✓

Common Mistakes

Avoid these frequent errors

Dividing by π instead of 2π
Don't divide 14 by just π = 14/π! This ignores the coefficient 2 in the formula 2πr and gives a radius that's twice as large. Always divide the circumference by the complete term 2π.

Practice Quiz

Test your knowledge with interactive questions

$$ r=2 $$

Calculate the circumference.

FAQ

Everything you need to know about this question

Why is my answer 7/π instead of a decimal?

Leaving the answer as $\frac{7}{\pi}$ is the exact form! Converting to decimal (≈ 2.23) gives an approximation. In mathematics, exact answers are often preferred over rounded decimals.

How do I remember the circumference formula?

Think of it as "2 times π times radius". The 2 comes from the fact that circumference is the distance around the circle, which relates to the diameter (2r).

What if I got 14π as my answer?

This means you multiplied instead of dividing! Remember: we're given the circumference (14) and need to find the radius, so we must divide by 2π to isolate r.

Can I use 3.14 instead of π?

You can, but your answer will be an approximation. Using π keeps the answer exact. If asked for a decimal approximation, then substitute π ≈ 3.14159.

Why do we divide both sides by 2π?

We need to isolate the variable r. Since r is multiplied by 2π in the equation 14 = 2πr, we divide both sides by 2π to get r by itself on one side.

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