Compare Circumferences: Circle A (8cm) vs Circle B (2cm) Diameter Problem

Q: Do I need to calculate the exact decimal value of π?

No! You can compare circumferences by looking at the coefficients. Since $ 8\pi > 2\pi $, Circle A is larger without calculating decimals.

Q: What if the diameters were really close, like 8cm and 7.9cm?

The same principle applies! $ 8\pi > 7.9\pi $ because 8 > 7.9. The larger diameter always gives the larger circumference since π is the same constant for both circles.

Q: Why don't I need to worry about the units?

Both diameters are in centimeters, so both circumferences will be in centimeters too. Since the units are the same, you can focus on comparing the numerical values.

Q: What if one circle had a much smaller diameter but was made of different material?

The material doesn't matter for circumference! Circumference depends only on the size (diameter), not what the circle is made of. A larger diameter always means a larger circumference.

Circle Circumference with Diameter Comparison

The diameter of circle A is 8 centimeters.

The diameter of circle B is 2 centimeters.

Which circle has a larger circumference?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:09 Which shape has a bigger perimeter?

00:12 Let's find the circle's perimeter using its diameter.

00:16 First, we'll use the perimeter formula for a circle.

00:27 Next, plug the circle's diameter into the formula and calculate.

00:32 And there you have it, this is the circle's perimeter.

00:35 Now, let's look at the second circle's diameter.

00:40 We'll use the same method to find this perimeter too.

00:46 Again, enter the diameter into the formula and solve.

00:53 Here you go, this is the perimeter for the second circle.

01:01 That's how you find which circle has a larger perimeter.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The diameter of circle A is 8 centimeters.

The diameter of circle B is 2 centimeters.

Which circle has a larger circumference?

Step-by-step solution

Let's solve the problem step-by-step:

Step 1: Calculate the circumference of circle A.
Step 2: Calculate the circumference of circle B.
Step 3: Compare the circumferences to determine which is larger.

Now, let's calculate each one:

Step 1: The circumference of circle A is calculated as follows:

Using the formula $C = \pi \times d$ ,

$C_A = \pi \times 8 = 8\pi$ cm.

Step 2: The circumference of circle B is calculated in the same manner:

Using the same formula $C = \pi \times d$ ,

$C_B = \pi \times 2 = 2\pi$ cm.

Step 3: Compare the circumferences:

Since $8\pi$ cm (Circle A) is clearly greater than $2\pi$ cm (Circle B), the circle with a larger circumference is Circle A.

Therefore, the circle with a larger circumference is Circle A.

Final Answer

Circle A

Key Points to Remember

Essential concepts to master this topic

Formula: Use C = π × d where d is diameter
Technique: Circle A: π × 8 = 8π, Circle B: π × 2 = 2π
Check: Compare coefficients: 8π > 2π since 8 > 2 ✓

Common Mistakes

Avoid these frequent errors

Confusing diameter with radius in calculations
Don't use C = π × r when given diameter = wrong formula gives wrong result! The diameter is twice the radius, so using radius formula with diameter doubles your answer incorrectly. Always use C = π × d when diameter is given.

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

Do I need to calculate the exact decimal value of π?

No! You can compare circumferences by looking at the coefficients. Since $8\pi > 2\pi$ , Circle A is larger without calculating decimals.

What if the diameters were really close, like 8cm and 7.9cm?

The same principle applies! $8\pi > 7.9\pi$ because 8 > 7.9. The larger diameter always gives the larger circumference since π is the same constant for both circles.

Why don't I need to worry about the units?

Both diameters are in centimeters, so both circumferences will be in centimeters too. Since the units are the same, you can focus on comparing the numerical values.

Can I use the radius formula instead?

Yes, but you'd need to convert first! Radius A = 4cm, Radius B = 1cm. Then $C_A = 2\pi(4) = 8\pi$ and $C_B = 2\pi(1) = 2\pi$ . Same result, but using diameter directly is faster.

What if one circle had a much smaller diameter but was made of different material?

The material doesn't matter for circumference! Circumference depends only on the size (diameter), not what the circle is made of. A larger diameter always means a larger circumference.

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