If the radius of a circle is halved, by what factor does the circumference decre

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Question: If the radius of a circle is halved, by what factor does the circumference decrease? (2020)

Options:

Correct Answer: 1/2

Exam Year: 2020

Solution:

Circumference = 2πr; If r is halved, new circumference = πr; Factor = 1/2.

If the radius of a circle is halved, by what factor does the circumference decrease? (2020)

If the radius of a circle is halved, by what factor does the circumference decrease? (2020)

Step 1: Understand the formula for the circumference of a circle, which is C = 2πr, where r is the radius.
Step 2: If the radius is halved, the new radius becomes r/2.
Step 3: Substitute the new radius into the circumference formula: C = 2π(r/2).
Step 4: Simplify the new circumference: C = 2π(r/2) = πr.
Step 5: Compare the new circumference (πr) to the original circumference (2πr).
Step 6: To find the factor of decrease, divide the new circumference by the original circumference: (πr) / (2πr) = 1/2.
Step 7: Conclude that the circumference decreases by a factor of 1/2.

Circumference of a Circle – The circumference of a circle is calculated using the formula C = 2πr, where r is the radius.
Effect of Radius on Circumference – Halving the radius directly affects the circumference, leading to a proportional decrease.