What is the formula for the area of a circle?

The formula for the area of a circle is given by Area = πr², where r represents the radius of the circle. This formula is derived from integral calculus and geometric principles.

To understand this, consider that the area of a circle encompasses all points that are a distance r from the center. The π (pi) in the formula represents the constant ratio of the circumference of any circle to its diameter, approximately equal to 3.14. When you square the radius (r²), it reflects the two-dimensional nature of area, where you multiply the length by the width. In this case, since a circle does not have distinct lengths as a rectangle does, the formula effectively expresses how the radius determines the entire area enclosed by the circle.

Other options present some components related to circles but do not correctly express the area:

• The formula for circumference is represented by 2πr, which pertains to the length around the circle rather than the space inside it.
• Area = πd involves the diameter, where d is equal to 2r; however, it does not reflect the most straightforward computation of area in terms of radius.
• The formula r² alone neglects the multiplication by π, which is crucial for accurately calculating the area