Which formula accurately represents the surface area of a circle?

The formula that accurately represents the surface area of a circle is derived from the relationship between the radius of the circle and its area. The surface area, or area, of a circle can be calculated using the formula πr², where r is the radius.

The first choice effectively presents this formula by breaking it down into components: it states π multiplied by the square of the radius. Since the radius is half of the diameter, dividing the diameter by 2 gives you the radius. Thus, when you apply this to the formula (π * (Diameter / 2) * (Diameter / 2)), you can observe that it simplifies to πr², confirming its validity for calculating the area of a circle.

The other options, while related to the context of the area, either do not express the area correctly or do so using a non-standard representation. The second option suggests a formula more akin to the circumference of a circle when multiplied by radius rather than giving an area. The third option presents the area correctly but does so in a less straightforward way. Therefore, the first choice stands as the most accurate representation of the surface area of a circle.