What is the formula for the area of a circle with radius r?

What is the formula for the area of a circle with radius r?

• A. A = πr^2
• B. A = 2πr
• C. A = πr
• D. A = πr^3

Answer: (A)

The area of a circle grows with the square of its radius, so the formula A = π r^2 expresses how much space is inside the circle. Here, π is a constant that relates linear dimensions to area for circles, and the r^2 term reflects how area changes when the circle scales in all directions. If you double the radius, the area increases by a factor of four, not just by two, because area is a two-dimensional measure. Compare the other forms: 2πr describes the circumference, the length around the circle. πr lacks the squared term, so it would have units of length, not area. πr^3 would have cubic units, which corresponds to volume, not area.

The area of a circle grows with the square of its radius, so the formula A = π r^2 expresses how much space is inside the circle. Here, π is a constant that relates linear dimensions to area for circles, and the r^2 term reflects how area changes when the circle scales in all directions. If you double the radius, the area increases by a factor of four, not just by two, because area is a two-dimensional measure.

Compare the other forms: 2πr describes the circumference, the length around the circle. πr lacks the squared term, so it would have units of length, not area. πr^3 would have cubic units, which corresponds to volume, not area.