What is the formula for the area of a circle?

What is the formula for the area of a circle?

• A. 2πr
• B. πd^2
• C. πr^2
• D. d^2/4

Answer: (C)

The area of a circle is the amount of space inside, and it grows with the square of the radius because when you scale a circle, the interior area increases by the square of that scale factor. The formula uses the radius: area equals π times the radius squared. The constant π comes from the circle’s geometry and connects linear dimensions to area through this squared relationship. If you know the diameter, you can substitute r = d/2 to get area = π(d/2)^2 = (π d^2)/4, showing how diameter relates to area. The other expressions either describe circumference (a linear measure around the edge) or leave out π, so they don’t give the true area. Therefore, the area is π r^2.

The area of a circle is the amount of space inside, and it grows with the square of the radius because when you scale a circle, the interior area increases by the square of that scale factor. The formula uses the radius: area equals π times the radius squared. The constant π comes from the circle’s geometry and connects linear dimensions to area through this squared relationship. If you know the diameter, you can substitute r = d/2 to get area = π(d/2)^2 = (π d^2)/4, showing how diameter relates to area. The other expressions either describe circumference (a linear measure around the edge) or leave out π, so they don’t give the true area. Therefore, the area is π r^2.