The area of a circle with radius r is given by which formula?

• A. A = π r^2
• B. P = 4s
• C. P = 2l + 2w
• D. P = a + b + c

Answer: (A)

The amount of space inside a circle is determined by multiplying the radius squared by π. This means the area grows with the square of the radius: if you double the radius, the area becomes four times larger. The constant π ties together the circle’s linear size with its enclosed area, since it appears in both the circumference formula and the area formula.

The other expressions describe perimeters, not areas: 4s is the perimeter of a square, 2l + 2w is the perimeter of a rectangle, and a sum of three sides isn’t a standard circle measure. So the correct formula for the circle’s area is A = π r^2.