Calculate Circle Radius: Finding r When C=35.6

Q: Why do we 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 equals 2 times π times the radius.

Q: What value of π should I use in calculations?

For most problems, use π ≈ 3.14 unless told otherwise. Some problems might ask for exact answers (leave π as π) or use π ≈ 3.14159 for more precision.

Q: How do I check if my radius answer is reasonable?

A good check is that the radius should be smaller than the circumference. Also, multiply your radius by about 6 - it should give you something close to the original circumference.

Q: What if I get a decimal answer - is that wrong?

Decimal answers are perfectly normal! Most circle problems result in decimal values. Just round to the number of decimal places requested or match the precision given in the problem.

Q: Can I use the diameter instead of radius?

Yes! Since diameter = 2r, you can find diameter first: $ d = \frac{C}{\pi} $, then divide by 2 to get radius. For C = 35.6: d = 35.6/3.14 ≈ 11.34, so r ≈ 5.67.

Circumference Formula with Radius Calculation

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

00:07 Let's find the circle's radius, called R.

00:11 We'll use the formula for the circumference of a circle.

00:20 Next, we'll plug in the given values to calculate R.

00:27 Let's focus on getting the radius, R, by itself.

00:38 Now, we substitute pi. Then calculate to find R.

00:53 And that's how we solve for the circle's radius. Great job!

Step-by-step written solution

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Understand the problem

Calculate the radius using the circumference given in the figure:

Step-by-step solution

We are tasked with finding the radius of a circle given its circumference, which is $C = 35.6$ units.

To do this, we start with the formula for circumference of a circle:
$C = 2\pi r$

Given: $C = 35.6$

We need to rearrange the formula to solve for the radius $r$ :
$r = \frac{C}{2\pi}$

Using $\pi \approx 3.14$ , we substitute the values we know into the formula:
$r = \frac{35.6}{2 \times 3.14}$

Calculate the denominator:
$2 \times 3.14 = 6.28$

Now, divide the circumference by this product:
$r = \frac{35.6}{6.28}$

Performing the division gives:
$r \approx 5.666$

Therefore, the radius of the circle is $r = 5.666$ .

Final Answer

5.666

Key Points to Remember

Essential concepts to master this topic

Formula: Use C = 2πr to relate circumference and radius
Technique: Rearrange to r = C/(2π) = 35.6/(2×3.14) = 5.666
Check: Verify by calculating C = 2π(5.666) ≈ 35.6 ✓

Common Mistakes

Avoid these frequent errors

Using the wrong formula or forgetting to divide by 2π
Don't use r = C/π or just divide by π = wrong answer like 11.3! This misses the factor of 2 in the circumference formula. Always use r = C/(2π) to get the correct radius.

Practice Quiz

Test your knowledge with interactive questions

O is the center of the circle in the diagram.

What is its perimeter?

FAQ

Everything you need to know about this question

Why do we 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 equals 2 times π times the radius.

What value of π should I use in calculations?

For most problems, use π ≈ 3.14 unless told otherwise. Some problems might ask for exact answers (leave π as π) or use π ≈ 3.14159 for more precision.

How do I check if my radius answer is reasonable?

A good check is that the radius should be smaller than the circumference. Also, multiply your radius by about 6 - it should give you something close to the original circumference.

What if I get a decimal answer - is that wrong?

Decimal answers are perfectly normal! Most circle problems result in decimal values. Just round to the number of decimal places requested or match the precision given in the problem.

Can I use the diameter instead of radius?

Yes! Since diameter = 2r, you can find diameter first: $d = \frac{C}{\pi}$ , then divide by 2 to get radius. For C = 35.6: d = 35.6/3.14 ≈ 11.34, so r ≈ 5.67.

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