Calculate the Radius When Circle Circumference is 80 Units

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

The circumference formula is $ C = 2\pi r $, not $ C = \pi r $. To isolate r, you must divide by the entire coefficient of r, which is 2π.

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

For better accuracy, use the π button on your calculator! Using 3.14 gives r = 12.739, while π gives r = 12.732, which matches the correct answer.

Q: How can I check if my radius is reasonable?

A quick estimate: if C = 80 and π ≈ 3, then $ r ≈ \frac{80}{2 \times 3} = \frac{80}{6} ≈ 13.3 $. Your answer of 12.732 should be close to this estimate.

Q: Do I need to memorize the value of π?

No! Always use your calculator's π button for accuracy. However, knowing π ≈ 3.14159 helps you estimate and check if your answer makes sense.

Circle Circumference 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

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

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

00:10 We'll substitute appropriate values according to the given data and calculate to find the radius

00:14 We'll isolate radius R

00:28 We'll substitute the value of pi and calculate to find radius R

00:38 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, we'll follow these steps:

Step 1: Identify the given information
Step 2: Apply the appropriate formula
Step 3: Perform the necessary calculations

Now, let's work through each step:
Step 1: The problem gives us the circumference $C = 80$ .
Step 2: We'll use the formula for the circumference of a circle: $C = 2\pi r$ .
Step 3: Substitute the given value into the formula and solve for $r$ :

$\begin{aligned} 80 &= 2\pi r \\ r &= \frac{80}{2\pi} \\ r &= \frac{80}{2 \times 3.14159} \\ r &= \frac{80}{6.28318} \\ r &= 12.732. \end{aligned}$

Therefore, the radius of the circle is $12.732$ .

Final Answer

12.732

Key Points to Remember

Essential concepts to master this topic

Formula: Use C = 2πr and solve by dividing circumference by 2π
Technique: Substitute C = 80 to get r = 80/(2π) = 12.732
Check: Verify: 2π(12.732) = 2(3.14159)(12.732) ≈ 80 ✓

Common Mistakes

Avoid these frequent errors

Using diameter formula instead of radius formula
Don't use C = πd directly and divide by π to get d = 25.465! This gives you the diameter, not radius. Always remember C = 2πr means r = C/(2π), not C/π.

Practice Quiz

Test your knowledge with interactive questions

$$ r=11 $$

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 $C = \pi r$ . To isolate r, you must divide by the entire coefficient of r, which is 2π.

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

For better accuracy, use the π button on your calculator! Using 3.14 gives r = 12.739, while π gives r = 12.732, which matches the correct answer.

What if I get a different decimal answer?

Check your calculation steps! Make sure you're dividing 80 by 2π (about 6.28318), not by π alone (about 3.14159). Small errors in the denominator create big differences.

How can I check if my radius is reasonable?

A quick estimate: if C = 80 and π ≈ 3, then $r ≈ \frac{80}{2 \times 3} = \frac{80}{6} ≈ 13.3$ . Your answer of 12.732 should be close to this estimate.

Do I need to memorize the value of π?

No! Always use your calculator's π button for accuracy. However, knowing π ≈ 3.14159 helps you estimate and check if your answer makes sense.

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