Calculate Circle Circumference: Finding Perimeter with 3 cm Radius

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

For circles, circumference and perimeter mean the same thing - the distance around the edge! We just use 'circumference' as the special term for circles.

Q: Should I calculate the decimal value or leave it as 6π?

Unless the problem asks for a decimal approximation, leave your answer as 6π cm. This gives the exact value, which is more precise than 18.84 cm.

Q: How do I remember the circumference formula?

Think: 'Circle goes around 2 times π times the radius' → C = 2πr. The '2' comes from diameter being twice the radius!

Q: What if I'm given the diameter instead of radius?

If you have diameter, either divide by 2 to get radius and use C = 2πr, or use the direct formula C = πd where d is diameter.

Circle Circumference with Given Radius

A circle has a radius of 3 cm.

What is its perimeter?

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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'll use the formula to calculate the circle's circumference

00:07 R value according to the given data

00:12 We'll substitute the R value and solve for the circumference

00:20 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

A circle has a radius of 3 cm.

What is its perimeter?

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the formula for the circumference of a circle as $C = 2\pi r$ .
Step 2: Substitute the known value of the radius into the formula.
Step 3: Simplify to find the circumference.

Now, let's work through each step:
Step 1: The formula for the circumference, $C$ , is $C = 2\pi r$ .
Step 2: Substitute the given radius $r = 3$ cm into the formula:
$C = 2\pi \times 3$ .
Step 3: Perform the multiplication:
$C = 6\pi$ .
Thus, the circumference of the circle is $6\pi$ cm.

Therefore, the solution to the problem is $6\pi$ cm.

Final Answer

$6\pi$ cm

Key Points to Remember

Essential concepts to master this topic

Formula: Circumference equals 2π times the radius (C = 2πr)
Technique: Substitute r = 3 into formula: C = 2π × 3 = 6π
Check: Verify radius is 3 cm, formula is correct, calculation gives 6π ✓

Common Mistakes

Avoid these frequent errors

Using area formula instead of circumference formula
Don't use A = πr² for finding perimeter = wrong measurement! Area measures space inside the circle, not distance around it. Always use C = 2πr for circumference (perimeter).

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 perimeter?

For circles, circumference and perimeter mean the same thing - the distance around the edge! We just use 'circumference' as the special term for circles.

Why do we use π in the formula?

π (pi) is the special ratio between a circle's circumference and its diameter. It's approximately 3.14, but we often leave it as π for exact answers.

Should I calculate the decimal value or leave it as 6π?

Unless the problem asks for a decimal approximation, leave your answer as 6π cm. This gives the exact value, which is more precise than 18.84 cm.

How do I remember the circumference formula?

Think: 'Circle goes around 2 times π times the radius' → C = 2πr. The '2' comes from diameter being twice the radius!

What if I'm given the diameter instead of radius?

If you have diameter, either divide by 2 to get radius and use C = 2πr, or use the direct formula C = πd where d is diameter.

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