Calculate Circle Radius When Circumference = 9: Using C = 2πr

Q: Why do I divide by 2π instead of just π?

The circumference formula is $ C = 2\pi r $, not $ C = \pi r $. The 2 comes from the fact that circumference is the distance around the entire circle, which involves both π and the diameter (2r).

Q: Should I use 3.14 or the π button on my calculator?

Use the π button on your calculator for more accurate results! Using 3.14 gives you approximations that may be slightly off from the expected answer.

Q: What if my answer doesn't match any of the choices exactly?

Circle problems often involve approximations due to π. Look for the answer choice that's closest to your calculated value, usually within 0.01-0.02 units.

Q: Do I need to memorize the rearranged formula?

It helps, but you can always start with $ C = 2\pi r $ and solve for r by dividing both sides by 2π. This way you understand the steps!

Circle Radius with Given Circumference

Calculate the radius using the circumference given in the figure:

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the circle's radius (R)

00:04 We'll use the formula for calculating circle circumference

00:09 We'll substitute appropriate values according to the given data and calculate to find the radius

00:20 We'll isolate radius R

00:30 We'll substitute the value of pi and calculate to find radius R

00:44 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

Calculate the radius using the circumference given in the figure:

Step-by-step solution

To solve this problem, let's go through the following steps:

Step 1: Identify the given information.
The circumference of the circle is given as $C = 9$ .
Step 2: Apply the circumference formula to solve for the radius.
The formula for circumference is $C = 2 \pi r$ , where $r$ is the radius.
Step 3: Solve for $r$ using the formula.
Rearrange the formula to solve for the radius: $r = \frac{C}{2\pi}$ .
Substituting the given value of the circumference, we have: $r = \frac{9}{2\pi} = \frac{9}{2 \times 3.14} = \frac{9}{6.28}.$
Step 4: Perform the arithmetic calculation.
By dividing, we get $r \approx 1.432.$

Therefore, the radius of the circle is approximately $1.432$ .

Final Answer

1.432

Key Points to Remember

Essential concepts to master this topic

Formula: Use C = 2πr, then rearrange to r = C/(2π)
Calculation: Substitute C = 9 to get r = 9/(2π) = 1.432
Check: Verify by computing 2π(1.432) ≈ 9.0 ✓

Common Mistakes

Avoid these frequent errors

Dividing circumference by π instead of 2π
Don't divide C by just π = r = 9/π = 2.86 (wrong answer)! This ignores the factor of 2 in the circumference formula. Always divide by 2π to find radius from circumference.

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 divide by 2π instead of just π?

The circumference formula is $C = 2\pi r$ , not $C = \pi r$ . The 2 comes from the fact that circumference is the distance around the entire circle, which involves both π and the diameter (2r).

Should I use 3.14 or the π button on my calculator?

Use the π button on your calculator for more accurate results! Using 3.14 gives you approximations that may be slightly off from the expected answer.

What if my answer doesn't match any of the choices exactly?

Circle problems often involve approximations due to π. Look for the answer choice that's closest to your calculated value, usually within 0.01-0.02 units.

How can I check if my radius is reasonable?

A quick check: multiply your radius by about 6 (since 2π ≈ 6.28). If you get close to the original circumference, your answer is reasonable!

Do I need to memorize the rearranged formula?

It helps, but you can always start with $C = 2\pi r$ and solve for r by dividing both sides by 2π. This way you understand the steps!

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