If the radius of a circle is halved, how does the circumference change? (2021)

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Question: If the radius of a circle is halved, how does the circumference change? (2021)

Options:

Correct Answer: Halved

Exam Year: 2021

Solution:

Circumference = 2πr. If radius is halved, new circumference = 2π(r/2) = πr, which is halved.

If the radius of a circle is halved, how does the circumference change? (2021)

If the radius of a circle is halved, how does the circumference change? (2021)

Step 1: Understand the formula for the circumference of a circle, which is C = 2πr, where r is the radius.
Step 2: Identify what happens when the radius is halved. If the original radius is r, the new radius will be r/2.
Step 3: Substitute the new radius into the circumference formula. The new circumference will be C = 2π(r/2).
Step 4: Simplify the new circumference. 2π(r/2) equals πr.
Step 5: Compare the new circumference (πr) to the original circumference (2πr). Notice that πr is half of 2πr.
Step 6: Conclude that when the radius is halved, the circumference is also halved.

Circumference of a Circle – Understanding the formula for the circumference of a circle (C = 2πr) and how changes in the radius affect it.