Circle Measurement Verification: Is 8m Circumference with 4m Diameter Possible?

Circle Properties with Pi Relationship

Is it possible that the circumference of a circle is 8 meters and its diameter is 4 meters?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Is it possible that the circumference of the circle equals 8?
00:03 Let's use the formula for calculating circle circumference, and isolate pi
00:08 We'll substitute appropriate values according to the given data and check the equality
00:14 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

Is it possible that the circumference of a circle is 8 meters and its diameter is 4 meters?

2

Step-by-step solution

To calculate, we will use the formula:

P2r=π \frac{P}{2r}=\pi

Pi is the ratio between the circumference of the circle and the diameter of the circle.

The diameter is equal to 2 radii.

Let's substitute the given data into the formula:

84=π \frac{8}{4}=\pi

2≠π 2\ne\pi

Therefore, this situation is not possible.

3

Final Answer

Impossible

Key Points to Remember

Essential concepts to master this topic
  • Pi Rule: Circumference divided by diameter always equals π (≈3.14)
  • Technique: Calculate C ÷ d = 8 ÷ 4 = 2
  • Check: Compare result to π: since 2 ≠ π, the measurements are impossible ✓

Common Mistakes

Avoid these frequent errors
  • Accepting measurements without checking the pi relationship
    Don't assume given measurements are automatically possible = wrong conclusions! Students often skip verification and miss that C ÷ d must equal π for any real circle. Always check if Cd=π \frac{C}{d} = \pi before accepting circle measurements.

Practice Quiz

Test your knowledge with interactive questions

There are only 4 radii in a circle.

FAQ

Everything you need to know about this question

Why can't a circle have circumference 8m and diameter 4m?

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Because every circle must follow the rule that circumference ÷ diameter = π. Since 8 ÷ 4 = 2, and 2 ≠ π (which is about 3.14), these measurements are mathematically impossible for a real circle.

What should the circumference be if the diameter is 4m?

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Use the formula C=πd C = \pi d . So C=π×4≈3.14×4=12.56 C = \pi \times 4 \approx 3.14 \times 4 = 12.56 meters. The circumference should be approximately 12.56 meters.

Is π always exactly 3.14?

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No! π is an irrational number that goes on forever: π = 3.14159265... We use 3.14 as an approximation, but the exact value never ends or repeats.

How do I remember that circumference ÷ diameter = π?

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Think of π as the "magic number" that tells you how many diameters fit around the circumference. It's always the same for every circle - about 3.14 diameters wrap around once!

What if I'm given radius instead of diameter?

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Remember that diameter = 2 × radius. So if radius is 2m, diameter is 4m. Then check if C2r=π \frac{C}{2r} = \pi or use C=2πr C = 2\pi r .

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