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

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

Options:

Correct Answer: It quadruples.

Solution:

If the radius is doubled, the area increases by a factor of four (since area is proportional to the square of the radius).

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

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

Step 1: Understand that the area of a circle is calculated using the formula A = πr², where A is the area and r is the radius.
Step 2: Identify the original radius of the circle, let's call it r.
Step 3: If the radius is doubled, the new radius becomes 2r.
Step 4: Substitute the new radius (2r) 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: This simplifies to A = 4(πr²), which shows that the new area is four times the original area.
Step 8: Conclude that when the radius is doubled, the area increases by a factor of four.

Area of a Circle – The area of a circle is calculated using the formula A = πr², where r is the radius.
Proportionality – Understanding that if the radius is multiplied by a factor, the area changes by the square of that factor.