In a circle, if the radius is halved, how does the area change?

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Question: In a circle, if the radius is halved, how does the area change?

Options:

Correct Answer: It is quartered

Solution:

Area = π * r². If radius is halved, area becomes π * (r/2)² = π * (r²/4) = (1/4) * original area.

In a circle, if the radius is halved, how does the area change?

In a circle, if the radius is halved, how does the area change?

Step 1: Understand the formula for the area of a circle, which is Area = π * r², where r is the radius.
Step 2: If the radius is halved, we write the new radius as r/2.
Step 3: Substitute the new radius into the area formula: Area = π * (r/2)².
Step 4: Calculate (r/2)², which is r²/4.
Step 5: Now, substitute this back into the area formula: Area = π * (r²/4).
Step 6: Simplify the equation: Area = (π * r²) / 4.
Step 7: Recognize that π * r² is the original area, so the new area is (1/4) of the original area.

Area of a Circle – Understanding the formula for the area of a circle (A = π * r²) and how changes in the radius affect the area.
Proportional Relationships – Recognizing how halving the radius leads to a quarter of the original area, illustrating the concept of proportionality.