Calculate Circle Circumference with Radius = 1/3: Step-by-Step Solution

Q: Why do I multiply by 2 in the circumference formula?

The formula C = 2πr comes from the relationship that circumference equals π times the diameter. Since diameter = 2r, we get C = π(2r) = 2πr.

Q: Should I leave my answer as a fraction or decimal?

Both $ \frac{2\pi}{3} $ (exact) and 2.094 (approximate) are correct! Use the exact form when possible, but convert to decimal when matching multiple choice answers.

Q: What if I forget the value of π?

Use π ≈ 3.14159 for calculations. Some problems give you π ≈ 3.14, which is fine too. The key is being consistent with whichever approximation you use.

Q: How do I work with the fraction 1/3 in calculations?

When multiplying by $ \frac{1}{3} $, remember: $ 2\pi \times \frac{1}{3} = \frac{2\pi}{3} $. Then divide: $ \frac{2 \times 3.14159}{3} = \frac{6.28318}{3} ≈ 2.094 $.

Q: Is there a difference between radius and diameter?

Radius (r): Distance from center to edgeDiameter (d): Distance across the circle through centerRemember: d = 2r, so always check which measurement you're given!

Circle Circumference with Fractional Radius

$r=\frac{1}{3}$

Calculate the circumference.

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate the circumference of the circle

00:03 We will use the formula for calculating circle circumference

00:06 We will substitute the radius according to the given data and solve for the circumference

00:12 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

$r=\frac{1}{3}$

Calculate the circumference.

Step-by-step solution

To solve this problem, we'll calculate the circumference of a circle using the formula $C = 2\pi r$ .

Step 1: Identify the given radius $r = \frac{1}{3}$ .
Step 2: Use the formula for circumference $C = 2\pi r$ .
Step 3: Substitute the radius into the formula: $C = 2\pi \times \frac{1}{3}$ .
Step 4: Simplify the expression to get $C = \frac{2\pi}{3}$ .
Step 5: Use an approximate value for $\pi \approx 3.14159$ to compute: $C \approx \frac{2 \times 3.14159}{3}$ .
Step 6: Calculate to obtain $C \approx 2.094$ .

Therefore, the circumference of the circle is approximately $2.094$ .

This matches choice 4 in the given multiple-choice answers.

Final Answer

2.094

Key Points to Remember

Essential concepts to master this topic

Formula: Use C = 2πr where π ≈ 3.14159
Technique: Substitute $r = \frac{1}{3}$ to get $C = \frac{2\pi}{3}$
Check: Calculate $\frac{2 \times 3.14159}{3} \approx 2.094$ ✓

Common Mistakes

Avoid these frequent errors

Using diameter formula instead of radius formula
Don't use C = πd when given the radius = wrong formula gives double the correct answer! Students often confuse radius and diameter formulas. Always use C = 2πr when given radius, or C = πd when given diameter.

Practice Quiz

Test your knowledge with interactive questions

$$ r=2 $$

Calculate the circumference.

FAQ

Everything you need to know about this question

Why do I multiply by 2 in the circumference formula?

The formula C = 2πr comes from the relationship that circumference equals π times the diameter. Since diameter = 2r, we get C = π(2r) = 2πr.

Should I leave my answer as a fraction or decimal?

Both $\frac{2\pi}{3}$ (exact) and 2.094 (approximate) are correct! Use the exact form when possible, but convert to decimal when matching multiple choice answers.

What if I forget the value of π?

Use π ≈ 3.14159 for calculations. Some problems give you π ≈ 3.14, which is fine too. The key is being consistent with whichever approximation you use.

How do I work with the fraction 1/3 in calculations?

When multiplying by $\frac{1}{3}$ , remember: $2\pi \times \frac{1}{3} = \frac{2\pi}{3}$ . Then divide: $\frac{2 \times 3.14159}{3} = \frac{6.28318}{3} ≈ 2.094$ .

Is there a difference between radius and diameter?

Radius (r): Distance from center to edge
Diameter (d): Distance across the circle through center
Remember: d = 2r, so always check which measurement you're given!

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Circle questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime