Question

what is the formula for the area of a circle?
a. a = πr²
b. a = πr
c. a = π²r
d. a = πd²

Explanation:

Step1: Recall circle - area formula

The area of a circle with radius $r$ is given by $A=\pi r^{2}$. Here, $\pi$ is a mathematical constant approximately equal to 3.14159, and $r$ is the radius of the circle. This formula is a well - known result in geometry.
The formula $A = \pi r$ is for the semi - circumference of a circle (not area). The formula $A=\pi^{2}r$ is not a valid formula for circle area. The formula $A = \pi d^{2}$ is incorrect as the correct formula in terms of diameter $d$ (where $d = 2r$) is $A=\pi(\frac{d}{2})^{2}=\frac{\pi d^{2}}{4}$.

Answer:

A. $A = \pi r^{2}$