What equation represents the area of a circle in terms of radius?

The equation that represents the area of a circle in terms of its radius is expressed as A = πr², where A is the area and r is the radius of the circle. The constant π (pi) is approximately equal to 3.14 and represents the ratio of the circumference of a circle to its diameter.

The formula indicates that the area is proportional to the square of the radius, highlighting how the area increases dramatically with increases in radius. This relationship makes the area a function of the radius squared, which is why the option stating A = @r² correctly captures the mathematical concept.

Other choices provided do not represent the area of a circle. For instance, the first option (A = bh) reflects the area formula for rectangles, involving base and height rather than a circular shape. The second choice (C = 2πr) describes the circumference of a circle, measuring the distance around it. The final option (f(x) = ax³ + bx² + cx + d) is a general polynomial equation and does not relate to the geometry of a circle at all.