Calculate Circle Circumference: Given Radius r=6 Units

Circle Circumference with Radius Calculation

r=6 r=6

Calculate the circumference.

666

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:04 Let's find the circumference of the circle.
00:07 We'll use the formula: Circumference equals 2 times pi times radius.
00:13 Now, let's substitute the radius into the formula and calculate the circumference.
00:18 And that's how we solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

r=6 r=6

Calculate the circumference.

666

2

Step-by-step solution

To solve this problem, follow these steps:

  • Step 1: Given that the radius r=6 r = 6 .
  • Step 2: Use the formula for the circumference of a circle, C=2πr C = 2\pi r .
  • Step 3: Substitute the radius into the formula: C=2π×6 C = 2\pi \times 6 .
  • Step 4: Calculate the expression: C=12π C = 12\pi .
  • Step 5: Approximate π3.14159 \pi \approx 3.14159 to find C12×3.14159 C \approx 12 \times 3.14159 .
  • Step 6: Perform the multiplication: C37.69908 C \approx 37.69908 .
  • Step 7: Round off the number to three decimal places: C37.699 C \approx 37.699 .

The correct answer matches the choice labeled 2: 37.699.

3

Final Answer

37.699

Key Points to Remember

Essential concepts to master this topic
  • Formula: Circumference equals 2πr 2\pi r where r is radius
  • Technique: Substitute given radius: C=2π×6=12π C = 2\pi \times 6 = 12\pi
  • Check: Use π3.14159 \pi \approx 3.14159 to get 12×3.1415937.699 12 \times 3.14159 \approx 37.699

Common Mistakes

Avoid these frequent errors
  • Using diameter instead of radius in formula
    Don't substitute the radius value into C=πd C = \pi d formula = wrong answer like 18.85! The diameter formula needs the diameter (12), not radius (6). Always use C=2πr C = 2\pi r when given the radius.

Practice Quiz

Test your knowledge with interactive questions

\( r=2 \)

Calculate the circumference.

222

FAQ

Everything you need to know about this question

What's the difference between the two circumference formulas?

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There are two formulas: C=2πr C = 2\pi r (using radius) and C=πd C = \pi d (using diameter). Since diameter = 2 × radius, both give the same result when used correctly!

Should I leave my answer as 12π or convert to decimal?

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It depends on what the question asks for! 12π 12\pi is the exact answer, while 37.699 is the approximate decimal. Multiple choice questions usually want the decimal approximation.

How many decimal places should I use for π?

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For most problems, π3.14159 \pi \approx 3.14159 gives enough precision. Using more decimal places won't significantly change your final answer for typical geometry problems.

What if I accidentally use the area formula instead?

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The area formula is A=πr2 A = \pi r^2 , which would give π×62=36π113.1 \pi \times 6^2 = 36\pi \approx 113.1 . This is much larger than circumference! Circumference measures the border, area measures the inside space.

How can I remember which formula to use?

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Think of it this way: Circumference is like a fence around a circular yard - you're measuring the border distance. Use C=2πr C = 2\pi r or C=πd C = \pi d depending on what measurement you're given.

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