What is the formula for the area of a circle?

What is the formula for the area of a circle?

• A. A = π • r²
• B. A = π • r
• C. A = 2π • r
• D. A = r²

Answer: (A)

Area is the amount of space inside a circle, and that space grows with the radius squared. The factor π ties the circle’s linear size to its two-dimensional area, so the area increases as the radius is squared. That gives A = π r^2. You can check with small numbers: a radius of 1 yields area π, a radius of 2 yields 4π. The other expressions don’t fit: π r has only linear units, 2π r is the circumference, and r^2 omits the essential π.

Area is the amount of space inside a circle, and that space grows with the radius squared. The factor π ties the circle’s linear size to its two-dimensional area, so the area increases as the radius is squared. That gives A = π r^2. You can check with small numbers: a radius of 1 yields area π, a radius of 2 yields 4π. The other expressions don’t fit: π r has only linear units, 2π r is the circumference, and r^2 omits the essential π.