Calculate Circle Circumference with Radius 8.5 Units: Step-by-Step Solution

Q: Why do we multiply by 2 in the circumference formula?

The circumference formula $ C = 2\pi r $ comes from the relationship between radius and diameter. Since diameter = 2 × radius, and circumference can also be written as $ C = \pi d $, we get $ C = \pi \times 2r = 2\pi r $.

Q: What value of pi should I use for calculations?

For most problems, use π ≈ 3.14159 for accurate results. Some textbooks use 3.14 for simpler calculations, but 3.14159 gives you the precision needed for decimal answers like 53.407.

Q: Is there a quick way to estimate if my answer is reasonable?

Yes! The circumference is always about 6 times the radius (since 2π ≈ 6.28). For radius 8.5: 6 × 8.5 = 51, so an answer around 53 makes perfect sense!

Q: What if I get confused between circumference and area?

Remember: Circumference is the distance around the circle (like a fence), while area is the space inside the circle (like a carpet). Circumference uses $ 2\pi r $, area uses $ \pi r^2 $.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate the circumference of the circle

00:03 Let's use the formula for calculating circle circumference

00:06 We'll substitute the radius according to the given data and solve for the circumference

00:12 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$r=8.5$

Calculate the circumference.

2

Step-by-step solution

To solve this problem, we'll use the formula for the circumference of a circle, which is:

$C = 2\pi r$

Given that the radius $r$ is 8.5, we substitute this value into the formula:

$C = 2 \pi \times 8.5$

Using the approximation $\pi \approx 3.14159$ , the formula becomes:

$C = 2 \times 3.14159 \times 8.5$

Calculate the multiplication:

$C = 53.40707$

After rounding to three decimal places, the circumference is $C = 53.407$ .

The circumference of the circle is therefore $53.407$ .

3

Final Answer

53.407

Key Points to Remember

Essential concepts to master this topic

Formula: Circumference equals two times pi times radius
Calculation: $C = 2 \times 3.14159 \times 8.5 = 53.407$
Check: Result should be about 6 times the radius: $53.407 \div 8.5 \approx 6.28$ ✓

Common Mistakes

Avoid these frequent errors

Using the area formula instead of circumference formula
Don't use $A = \pi r^2$ when asked for circumference = $3.14159 \times 8.5^2 = 226.98$ ! This gives the area inside the circle, not the distance around it. Always use $C = 2\pi r$ for 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 we multiply by 2 in the circumference formula?

+

The circumference formula $C = 2\pi r$ comes from the relationship between radius and diameter. Since diameter = 2 × radius, and circumference can also be written as $C = \pi d$ , we get $C = \pi \times 2r = 2\pi r$ .

What value of pi should I use for calculations?

+

For most problems, use π ≈ 3.14159 for accurate results. Some textbooks use 3.14 for simpler calculations, but 3.14159 gives you the precision needed for decimal answers like 53.407.

How do I know if I should round my answer?

+

Look at the answer choices! In this problem, all options have 3 decimal places, so round your final answer to match. Calculate with full precision first, then round at the very end.

Is there a quick way to estimate if my answer is reasonable?

+

Yes! The circumference is always about 6 times the radius (since 2π ≈ 6.28). For radius 8.5: 6 × 8.5 = 51, so an answer around 53 makes perfect sense!

What if I get confused between circumference and area?

+

Remember: Circumference is the distance around the circle (like a fence), while area is the space inside the circle (like a carpet). Circumference uses $2\pi r$ , area uses $\pi r^2$ .

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Calculate Circle Circumference with Radius 8.5 Units: Step-by-Step Solution

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