Which formula gives the area of a circle?

• A. a = πr
• B. a = 2πr
• C. a = πr^2
• D. a = r^2

Answer: (C)

Area is the amount of space inside a circle, and it grows with the square of the radius. The circle’s area is π times the radius squared because when you measure how much surface the circle covers, you multiply a constant (π) by the radius length twice (r × r). This gives the correct units and scale for area.

The correct expression, π times the radius squared, reflects that relationship. The other common formulas aren’t area: one gives a length, not area; another gives the distance around the circle; and omitting π misses a essential factor needed to measure area.