Calculate Radius from Circumference: Finding r When C = 400

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

The circumference formula is $ C = 2\pi r $, not $ C = \pi r $. To solve for radius, you must divide by everything that's multiplying r, which is 2π.

Q: Should I use 3.14 or 3.14159 for π?

For better accuracy, use 3.14159 or your calculator's π button. Using just 3.14 can give you a less precise answer that might not match the expected result.

Q: How can I check if my radius answer is correct?

Substitute back! Calculate $ 2\pi r $ using your radius value. If you get approximately 400, your answer is correct!

Q: Why is my answer a decimal instead of a whole number?

That's normal! Most real-world circle problems give decimal answers because π is irrational. Round to the precision asked for in the problem.

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)

00:03 We will use the formula for calculating circle circumference

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

00:19 We will isolate radius R

00:31 We will substitute the value of pi and calculate to find radius R

00:42 And this is the solution to the question

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 the problem, we'll follow these steps:

Step 1: Identify the given information.
Step 2: Apply the circumference formula to find the radius.
Step 3: Perform the necessary calculations to obtain the radius.

Now, let's work through each step:

Step 1: We know from the problem statement that the circumference of the circle is $C = 400$ .

Step 2: We'll use the formula for the circumference of a circle: $C = 2\pi r$ .

Step 3: Solving for $r$ , we have: $r = \frac{C}{2\pi} = \frac{400}{2\pi}.$ Substituting $\pi \approx 3.14159$ , $r = \frac{400}{2 \times 3.14159} = \frac{400}{6.28318} \approx 63.662.$

Therefore, the radius of the circle is approximately $\mathbf{63.662}$ .

Final Answer

63.662

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) = 400/(2×3.14159)
Check: Verify by calculating 2π(63.662) ≈ 400 ✓

Common Mistakes

Avoid these frequent errors

Using diameter formula instead of radius
Don't use C = πd directly and forget to divide by 2! This gives you the diameter (127.324), not the radius. Always remember that radius = diameter ÷ 2, so use r = C/(2π) for radius calculations.

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 solve for radius, you must divide by everything that's multiplying r, which is 2π.

Should I use 3.14 or 3.14159 for π?

For better accuracy, use 3.14159 or your calculator's π button. Using just 3.14 can give you a less precise answer that might not match the expected result.

How can I check if my radius answer is correct?

Substitute back! Calculate $2\pi r$ using your radius value. If you get approximately 400, your answer is correct!

What if I get the diameter by mistake?

If your answer seems too large (like 127 instead of 64), you probably calculated the diameter. Just divide your result by 2 to get the radius!

Why is my answer a decimal instead of a whole number?

That's normal! Most real-world circle problems give decimal answers because π is irrational. Round to the precision asked for in the problem.

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