Circle Measurement: Proving Diameter = 2 × Radius (5cm to 10cm)

Diameter Calculation with Basic Circle Formula

If the radius of a circle is 5 cm, then the length of the diameter is 10 cm.

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Step-by-step written solution

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1

Understand the problem

If the radius of a circle is 5 cm, then the length of the diameter is 10 cm.

2

Step-by-step solution

To determine if the statement "If the radius of a circle is 5 cm, then the length of the diameter is 10 cm" is true, we need to use the relationship between the radius and diameter of a circle.

The diameter d d of a circle is calculated using the formula:

d=2r d = 2r

where r r is the radius. In this problem, the radius r r is given as 5 cm.

Using the formula, the diameter is:

d=2×5cm=10cm d = 2 \times 5 \, \text{cm} = 10 \, \text{cm}

This matches exactly the length of the diameter given in the problem.

Therefore, the statement "If the radius of a circle is 5 cm, then the length of the diameter is 10 cm" is True.

3

Final Answer

True

Key Points to Remember

Essential concepts to master this topic
  • Formula: Diameter equals two times the radius: d = 2r
  • Calculation: Multiply radius by 2: 5 cm × 2 = 10 cm
  • Check: Verify diameter is exactly twice the radius length ✓

Common Mistakes

Avoid these frequent errors
  • Confusing radius and diameter definitions
    Don't think radius = diameter or use d = r instead of d = 2r = wrong measurements! This gives answers that are half the correct size. Always remember diameter is the full distance across the circle through the center.

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

What's the difference between radius and diameter?

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The radius is the distance from the center to the edge of the circle. The diameter is the full distance across the circle through the center - it's always exactly twice the radius!

Why is the diameter always 2 times the radius?

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Think of it this way: the diameter goes from one side of the circle to the other, passing through the center. That means it covers two radius lengths - one from edge to center, then another from center to the opposite edge.

How can I remember the formula d = 2r?

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Remember: Diameter = 2 × Radius, or think "Double the Radius" to get the diameter. The diameter is always the bigger measurement!

What if I'm given the diameter and need the radius?

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Just work backwards! If d=2r d = 2r , then r=d2 r = \frac{d}{2} . Divide the diameter by 2 to get the radius.

Do all circles follow this d = 2r rule?

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Yes, absolutely! Every single circle, no matter how big or small, follows this rule. It's one of the most reliable formulas in geometry - the diameter is always exactly twice the radius.

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