If the radius of a circle is doubled, what happens to its area? (2020)

If the radius of a circle is doubled, what happens to its area? (2020)

Step 1: Understand the formula for the area of a circle, which is A = 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 into the area formula. The new area A' is A' = π(2r)².
Step 4: Calculate (2r)². This equals 4r².
Step 5: Substitute 4r² back into the area formula. So, A' = π(4r²) = 4πr².
Step 6: Compare the new area A' with the original area A. The new area A' is 4 times the original area A.

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 Effects – Recognizing how geometric properties scale with changes in dimensions, specifically how area scales with the square of the radius.