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

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

Answer: (B)

The area of a circle grows with the square of the radius, because both dimensions of the circle scale with r, so the space inside increases as r^2. The area is given by A = πr^2, where A is the area and r is the radius. The constant π reflects the circle’s geometry and appears in formulas for both area and circumference. For example, with a radius of 3 units, the area is π × 9 ≈ 28.27 square units, showing why squaring the radius is essential. The other expressions describe length around the circle or mix up symbols, so they don’t yield the area. Thus, the correct formula is A = πr^2.