If a circle's radius is doubled, how does its area change? (2020)

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Question: If a circle\'s radius is doubled, how does its area change? (2020)

Options:

Correct Answer: It quadruples

Exam Year: 2020

Solution:

Area = πr². If radius is doubled (2r), new area = π(2r)² = 4πr², which is quadruple the original area.

If a circle's radius is doubled, how does its area change? (2020)

If a circle's radius is doubled, how does its area change? (2020)

Step 1: Understand the formula for the area of a circle, which is Area = πr², where r is the radius.
Step 2: Identify what happens when the radius is doubled. If the original radius is r, the new radius becomes 2r.
Step 3: Substitute the new radius (2r) into the area formula. The new area becomes Area = π(2r)².
Step 4: Calculate (2r)². This equals 4r².
Step 5: Now substitute this back into the area formula: Area = π(4r²).
Step 6: Simplify the new area to get Area = 4πr².
Step 7: Compare the new area (4πr²) to the original area (πr²). The new area is 4 times the original area.

Area of a Circle – Understanding the formula for the area of a circle (A = πr²) and how changes in the radius affect the area.
Scaling Properties – Recognizing how geometric properties scale with changes in dimensions, specifically how area scales with the square of the radius.