Calculate Circle Circumference: Finding Distance with 6-Unit Radius

Q: What's the difference between circumference and area?

Circumference is the distance around the circle (like a fence around it), while area is the space inside the circle. Use C = 2πr for circumference and A = πr² for area.

Q: What if the problem gives me the diameter instead?

If you have diameter, use C = πd directly! Or divide diameter by 2 to get radius, then use C = 2πr. Both methods give the same answer.

Q: How can I remember the circumference formula?

Think "2 π r" - Two Pies with Radius! Or remember that circumference has an 'r' sound, so it uses radius in the formula.

Circle Circumference with Given Radius

Look at the circle in the figure.

What is its circumference if its radius is equal to 6?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the circumference of the circle

00:03 We will use the formula to calculate the circumference of a circle

00:11 We will substitute the radius value according to the given data and solve for the circumference

00:26 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Look at the circle in the figure.

What is its circumference if its radius is equal to 6?

Step-by-step solution

Formula of the circumference:

$P=2\pi r$

We insert the given data into the formula:

$P=2\times6\times\pi$

$P=12\pi$

Final Answer

$12\pi$

Key Points to Remember

Essential concepts to master this topic

Formula: Circumference equals 2πr where r is the radius
Calculation: Substitute r = 6 into C = 2π(6) = 12π
Check: Verify radius times 2π gives 6 × 2π = 12π ✓

Common Mistakes

Avoid these frequent errors

Using area formula instead of circumference formula
Don't use πr² = π(6)² = 36π for circumference! This is the area formula and gives a completely different answer. Always use C = 2πr for the distance around a circle.

Practice Quiz

Test your knowledge with interactive questions

$$ r=2 $$

Calculate the circumference.

FAQ

Everything you need to know about this question

What's the difference between circumference and area?

Circumference is the distance around the circle (like a fence around it), while area is the space inside the circle. Use C = 2πr for circumference and A = πr² for area.

Do I need to calculate the decimal value of 12π?

Usually no! Most problems want the exact answer with π in it. Only calculate the decimal approximation if specifically asked, like "round to the nearest tenth."

Why do we multiply the radius by 2?

The radius goes from center to edge, but circumference goes all the way around. Since diameter = 2 × radius, and circumference = π × diameter, we get C = π(2r) = 2πr.

What if the problem gives me the diameter instead?

If you have diameter, use C = πd directly! Or divide diameter by 2 to get radius, then use C = 2πr. Both methods give the same answer.

How can I remember the circumference formula?

Think "2 π r" - Two Pies with Radius! Or remember that circumference has an 'r' sound, so it uses radius in the formula.

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