If the radius of a circle is doubled, how does the area change? (2021)

If the radius of a circle is doubled, how does the area change? (2021)

Step 1: Understand the formula for the area of a circle, which is Area = πr², where r is the radius.
Step 2: If the radius is doubled, we replace r with 2r in the formula.
Step 3: Substitute 2r into the area formula: Area = π(2r)².
Step 4: Calculate (2r)², which is 4r².
Step 5: Now the area formula becomes Area = π(4r²).
Step 6: Simplify the area formula to Area = 4πr².
Step 7: Compare the new area (4πr²) to the original area (πr²).
Step 8: Notice that the new area is 4 times the original area, meaning it quadruples.

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 when dimensions are changed, specifically how area scales with the square of the radius.