To find the correct formula for the area of a circle, we need to understand what each term in the multiple-choice answers represents.
1. A. [tex]$A=\pi d^2$[/tex]
- [tex]\(d\)[/tex] represents the diameter of the circle.
- The formula uses [tex]\(d^2\)[/tex], but the correct formula does not.
2. B. [tex]$A=\pi r^2$[/tex]
- [tex]\(r\)[/tex] represents the radius of the circle.
- The formula includes [tex]\(\pi\)[/tex] multiplied by the square of the radius, which aligns with the definition of the area of a circle.
3. C. [tex]$A=\pi^2 r$[/tex]
- This option includes [tex]\(\pi^2\)[/tex], suggesting [tex]\(\pi\)[/tex] squared, which is incorrect.
- The radius is not squared in this formula, which is also incorrect.
4. D. [tex]$A=\pi r$[/tex]
- This option includes [tex]\(\pi\)[/tex] multiplied by the radius, which is incomplete and incorrect.
The correct formula for the area of a circle is found in option B:
[tex]\[ A = \pi r^2 \][/tex]
So, the answer to the question "What is the formula for the area of a circle?" is:
B. [tex]$A=\pi r^2$[/tex]
