Calculate Circle Radius: Converting 50.25 Circumference

Circumference Formula with Radius Solving

A circle has a circumference of 50.25.

What is its radius?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the radius
00:03 We'll use the formula for calculating circle circumference
00:08 We'll substitute appropriate values according to the given data and solve for the radius
00:14 We'll substitute the value of pi
00:26 We'll isolate radius R and calculate
00:39 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

A circle has a circumference of 50.25.

What is its radius?

2

Step-by-step solution

We use the formula:

P=2πr P=2\pi r

We insert the known data into the formula:

50.25=3.14×2r 50.25=3.14\times2r

50.25=2×r×3.14 50.25=2\times r\times3.14

50.25=6.28r 50.25=6.28r

50.256.28=6.28r6.28 \frac{50.25}{6.28}=\frac{6.28r}{6.28}

r=8 r=8

3

Final Answer

8

Key Points to Remember

Essential concepts to master this topic
  • Formula: Use C = 2πr to relate circumference and radius
  • Technique: Substitute π ≈ 3.14, so 50.25 = 6.28r
  • Check: Verify 2 × 3.14 × 8 = 50.24 ≈ 50.25 ✓

Common Mistakes

Avoid these frequent errors
  • Using wrong formula or incorrect π value
    Don't confuse circumference C = 2πr with area A = πr² or use π = 3 instead of 3.14! This gives completely wrong answers like r = 16.75 instead of 8. Always use C = 2πr with π ≈ 3.14 for circumference problems.

Practice Quiz

Test your knowledge with interactive questions

\( r=2 \)

Calculate the circumference.

222

FAQ

Everything you need to know about this question

Why do we use π = 3.14 instead of the exact value?

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π ≈ 3.14 is a common approximation that makes calculations easier. For most practical problems, this gives sufficiently accurate results. You might also see π ≈ 3.14159 for more precision.

What's the difference between circumference and area formulas?

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Circumference measures the distance around the circle using C=2πr C = 2\pi r . Area measures the space inside using A=πr2 A = \pi r^2 . Don't mix them up!

How do I isolate r from C = 2πr?

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Divide both sides by 2π 2\pi : r=C2π r = \frac{C}{2\pi} . With π = 3.14, this becomes r=C6.28 r = \frac{C}{6.28} .

Why doesn't my answer come out exactly 8?

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Since we're using π ≈ 3.14 instead of the exact value, calculations may have small rounding differences. Getting 7.99 or 8.01 is normal - round to the nearest whole number when appropriate.

Can I use a calculator for π?

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Yes! Most calculators have a π button that gives more decimal places. However, for this problem using π = 3.14 matches the expected answer format.

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