For the given circle, which of these choices is true regarding its circumference and area?

A.
The circumference is larger, and it is two times the area.
B.
The area is larger, and it is two times the circumference.
C.
The area is larger, and it is four times the circumference.
D.
The circumference is larger, and it is four times the area.

1 answer

C. The area is larger, and it is four times the circumference.

The formula for the circumference of a circle is 2πr, where r is the radius, and the formula for the area of a circle is πr^2. Therefore, the area is π times the radius squared, and the circumference is 2π times the radius. Since the area formula includes a radius squared term, the area will generally be larger than the circumference for a given circle. In this case, the area is four times the circumference.