Calculate Circle Circumference: Using Given Radius Length of 8

Circumference Formula with Given Radius

O is the center of the circle in the figure below.

888OOO What is its circumference?

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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 Radius - the line segment connecting the center of the circle with a point on its circumference
00:06 We will use the formula to calculate the circle's circumference
00:10 We will substitute the value of R and solve for the circumference
00:18 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

O is the center of the circle in the figure below.

888OOO What is its circumference?

2

Step-by-step solution

We use the formula:P=2πr P=2\pi r

We replace the data in the formula:P=2×8π P=2\times8\pi

P=16π P=16\pi

3

Final Answer

16π 16\pi cm

Key Points to Remember

Essential concepts to master this topic
  • Formula: Circumference equals 2π times radius (C = 2πr)
  • Calculation: Substitute r = 8: C = 2 × π × 8 = 16π
  • Check: Radius 8 gives circumference 16π ≈ 50.27 units ✓

Common Mistakes

Avoid these frequent errors
  • Using area formula instead of circumference formula
    Don't use A = πr² for circumference problems = gets 64π instead of 16π! The area formula gives you square units, not the distance around. Always use C = 2πr for circumference calculations.

Practice Quiz

Test your knowledge with interactive questions

O is the center of the circle in the diagram.

What is its perimeter?

444OOO

FAQ

Everything you need to know about this question

Why do we multiply by 2 in the circumference formula?

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The circumference formula C = 2πr comes from the fact that circumference = π × diameter. Since diameter = 2 × radius, we get C = π × (2r) = 2πr.

Should I leave my answer as 16π or convert to decimal?

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Keep it as 16π unless specifically asked for a decimal! The exact form with π is more precise than rounding to 50.27.

What's the difference between circumference and area?

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Circumference measures the distance around the circle (like a fence), while area measures the space inside the circle (like grass in a yard).

How do I remember which formula to use?

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Think of circumference as the 'rim' of the circle. Since it's a distance, use C = 2πr. Area fills the inside, so it needs r² (A = πr²).

What if I don't have π on my calculator?

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You can use π ≈ 3.14159, but it's usually better to leave answers in exact form with π unless told otherwise. Many problems expect the π to remain.

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