Calculate Circle Circumference with Radius 8.7: Step-by-Step Solution

Q: Why do we multiply by 2π instead of just π?

The circumference is the distance around the circle. Since the diameter is twice the radius, and circumference is π times diameter, we get $ C = \pi d = \pi (2r) = 2\pi r $.

Q: Should I use 3.14 or 3.14159 for π?

Use 3.14159 for more accurate results! Using just 3.14 gives you 54.636, which is close but not as precise as 54.664.

Q: What if I get a different decimal answer?

Check your calculation step by step: 2 × 3.14159 × 8.7. Make sure you're multiplying in the right order and not missing any decimal places!

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate the circle's circumference

00:03 We'll use the formula to calculate the circle's circumference

00:07 We'll substitute the given radius and solve for the circumference

00:11 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

$r=8.7$

Calculate the circumference.

2

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: We are given the radius of the circle $r = 8.7$ .

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

Step 3: Plugging in our value for the radius, we calculate:
$C = 2 \pi (8.7)$

Using $\pi \approx 3.14159$ , the expression becomes:
$C = 2 \times 3.14159 \times 8.7$

Performing the multiplication, we get:
$C \approx 54.664$

Therefore, the circumference of the circle is approximately $54.664$ .

This matches the answer choice : 54.664

, confirming its correctness.

3

Final Answer

54.664

Key Points to Remember

Essential concepts to master this topic

Formula: Circumference equals 2π times the radius
Technique: Calculate $C = 2 \times 3.14159 \times 8.7 = 54.664$
Check: Divide result by 2π to get back 8.7 radius ✓

Common Mistakes

Avoid these frequent errors

Confusing circumference and area formulas
Don't use $\pi r^2$ for circumference = wrong answer like 237.7! That's the area formula, not circumference. Always use $C = 2\pi r$ for circumference.

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 multiply by 2π instead of just π?

+

The circumference is the distance around the circle. Since the diameter is twice the radius, and circumference is π times diameter, we get $C = \pi d = \pi (2r) = 2\pi r$ .

Should I use 3.14 or 3.14159 for π?

+

Use 3.14159 for more accurate results! Using just 3.14 gives you 54.636, which is close but not as precise as 54.664.

What if I get a different decimal answer?

+

Check your calculation step by step: 2 × 3.14159 × 8.7. Make sure you're multiplying in the right order and not missing any decimal places!

How can I check if 54.664 is reasonable?

+

Think about it: the radius is 8.7, so the diameter is 17.4. Since circumference is slightly more than 3 times the diameter, expect around 3 × 17.4 = 52.2. Our answer 54.664 makes sense!

Do I need to include units in my answer?

+

If the radius has units (like cm or inches), then your circumference should have the same units. If no units are given, just write the number like 54.664.

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Calculate Circle Circumference with Radius 8.7: Step-by-Step Solution

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