What is the formula for the area of a circle?

A. [tex]A=\pi d^2[/tex]

B. [tex]A=\pi r^2[/tex]

C. [tex]A=\pi^2 r[/tex]

D. [tex]A=\pi r[/tex]



Answer :

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]