What is the formula for the area of a circle?

What is the formula for the area of a circle?

• A. πr^2
• B. 2πr
• C. πd^2
• D. 2πd

Answer: (A)

Area is the amount of space inside a circle, and for a circle the space inside grows with the square of the radius. The constant π links this size to the radius, so the area is π times r squared. This makes sense: if you double the radius, the area becomes four times larger, which matches the r^2 relation. The other formulas describe different quantities: 2πr is the circumference, the distance around the circle; πd^2 would become four times larger than the area when you replace d with 2r, since πd^2 = π(2r)^2 = 4πr^2; 2πd is not the area either. So the correct expression for the area with the radius given is πr^2.

Area is the amount of space inside a circle, and for a circle the space inside grows with the square of the radius. The constant π links this size to the radius, so the area is π times r squared. This makes sense: if you double the radius, the area becomes four times larger, which matches the r^2 relation. The other formulas describe different quantities: 2πr is the circumference, the distance around the circle; πd^2 would become four times larger than the area when you replace d with 2r, since πd^2 = π(2r)^2 = 4πr^2; 2πd is not the area either. So the correct expression for the area with the radius given is πr^2.