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In a circle, if the radius is doubled, how does the circumference change?

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Question: In a circle, if the radius is doubled, how does the circumference change?

Options:

  1. It doubles
  2. It triples
  3. It quadruples
  4. It remains the same

Correct Answer: It doubles

Solution: 

The circumference of a circle is given by C = 2πr. If the radius is doubled, the new circumference is C = 2π(2r) = 4πr, which is double the original circumference.

In a circle, if the radius is doubled, how does the circumference change?

Practice Questions

Q1
In a circle, if the radius is doubled, how does the circumference change?
  1. It doubles
  2. It triples
  3. It quadruples
  4. It remains the same

Questions & Step-by-Step Solutions

In a circle, if the radius is doubled, how does the circumference change?
  • Step 1: Understand that the circumference of a circle is calculated using the formula C = 2πr, where r is the radius.
  • Step 2: Identify the original radius of the circle, which we will call 'r'.
  • Step 3: If the radius is doubled, the new radius becomes '2r'.
  • Step 4: Substitute the new radius into the circumference formula: C = 2π(2r).
  • Step 5: Simplify the equation: C = 4πr.
  • Step 6: Compare the new circumference (4πr) to the original circumference (2πr).
  • Step 7: Notice that 4πr is double the original circumference (2πr).
  • Circumference of a Circle – Understanding the formula C = 2πr and how changes in the radius affect the circumference.
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