The radius of a circle is doubled. Which of the following describes the effect of this change on the area?

Question

UpStudy AI · Accepted Answer

1. The area $$ A $$ of a circle with radius $$ r $$ is given by:
   $$
   A = \pi r^2
   $$

2. If the radius is doubled, the new radius becomes $$ 2r $$.

3. Substitute the new radius into the area formula:
   $$
   A_{\text{new}} = \pi (2r)^2
   $$

4. Simplify the expression:
   $$
   A_{\text{new}} = \pi (4r^2) = 4\pi r^2
   $$

5. Since the original area is $$ \pi r^2 $$, the new area is:
   $$
   A_{\text{new}} = 4A
   $$

The area of the circle is quadrupled.
The area of the circle becomes four times larger.

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