In a circle, if the radius is doubled, what happens to the area of the circle?

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Question: In a circle, if the radius is doubled, what happens to the area of the circle?

Options:

Correct Answer: It quadruples

Solution:

The area of a circle is given by A = πr². If the radius is doubled, the new area becomes π(2r)² = 4πr², which is four times the original area.

In a circle, if the radius is doubled, what happens to the area of the circle?

In a circle, if the radius is doubled, what happens to the area of the circle?

Step 1: Understand that the area of a circle is calculated using the formula A = πr², where r is the radius.
Step 2: Identify the original radius of the circle as r.
Step 3: If the radius is doubled, the new radius becomes 2r.
Step 4: Substitute the new radius into the area formula: A = π(2r)².
Step 5: Calculate (2r)², which equals 4r².
Step 6: Now, substitute this back into the area formula: A = π(4r²).
Step 7: Simplify the equation to get A = 4πr².
Step 8: Compare the new area (4πr²) to the original area (πr²) to see that the new area is four times the original area.

Area of a Circle – Understanding the formula A = πr² and how changes in the radius affect the area.