Calculate Circle Radius from Circumference 31.41: Using C = 2πr

Circle Formula with Radius Isolation

A circle has a circumference of 31.41.

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
00:09 We'll substitute appropriate values according to the given data and solve for the radius
00:15 We'll substitute the value of pi
00:29 We'll isolate radius R and calculate
00:43 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 31.41.

What is its radius?

2

Step-by-step solution

To solve the exercise, first we must remember the circumference formula:

P=2πR P= 2\pi R

P is the circumference and Pi has a value of 3.14 (approximately).

We substitute in the known data:

31.41=23.141R 31.41=2\cdot3.141\cdot R

Keep in mind that the result can be easily simplified using Pi:

31.413.141=2R \frac{31.41}{3.141}=2R

10=2R 10=2R

Finally, we simplify by 2:

5=R 5=R

3

Final Answer

5

Key Points to Remember

Essential concepts to master this topic
  • Formula: Use C = 2πr to find radius from circumference
  • Technique: Divide circumference by 2π: 31.41 ÷ 6.282 = 5
  • Check: Substitute back: 2π(5) = 31.41 matches given circumference ✓

Common Mistakes

Avoid these frequent errors
  • Dividing circumference by π instead of 2π
    Don't divide 31.41 by 3.14 = 10! This gives diameter, not radius, because you forgot the factor of 2 in the formula. Always divide the circumference by 2π to isolate the radius properly.

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 I divide by 2π instead of just π?

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The circumference formula is C = 2πr, not C = πr. To isolate r, you must divide by the entire coefficient . Think of it as undoing multiplication!

Should I use 3.14 or 3.141 for π?

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Use the value that matches your given circumference! Here, 31.41 ÷ 6.282 = 5 exactly, so 3.141 gives the cleanest answer. More decimal places mean more precision.

What's the difference between radius and diameter?

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Radius goes from center to edge (what we're finding). Diameter goes all the way across and equals 2 × radius. Don't confuse them!

How can I check if my radius is reasonable?

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A quick check: if radius = 5, then diameter = 10. Does a circle with diameter 10 having circumference 31.41 make sense? Yes, since circumference ≈ 3 × diameter!

What if I get a messy decimal for the radius?

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That's normal! Real-world problems often have decimal answers. Just round appropriately (usually 1-2 decimal places) and always check your work.

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