What is the formula for the area of a circle?

What is the formula for the area of a circle?

• A. V=4/3πr³
• B. A=2πrh
• C. V=πr²
• D. A=πr²

Answer: (D)

The main idea is that the space inside a circle grows with the square of its radius. Area is a two‑dimensional measure, so when you scale the circle, the area doesn’t just double or triple—it grows with r^2. The constant that ties area to r^2 is π, which comes from the circle’s geometry and its relationship between circumference and diameter. Putting this together, the area inside a circle is π times the radius squared. This also fits intuitive checks: if the radius is 1, the area is π square units; doubling the radius makes the area four times larger, since (2r)^2 = 4r^2. The other provided expressions correspond to different quantities (like volume or lateral surface area) and do not describe the interior area of a circle.

The main idea is that the space inside a circle grows with the square of its radius. Area is a two‑dimensional measure, so when you scale the circle, the area doesn’t just double or triple—it grows with r^2. The constant that ties area to r^2 is π, which comes from the circle’s geometry and its relationship between circumference and diameter. Putting this together, the area inside a circle is π times the radius squared. This also fits intuitive checks: if the radius is 1, the area is π square units; doubling the radius makes the area four times larger, since (2r)^2 = 4r^2. The other provided expressions correspond to different quantities (like volume or lateral surface area) and do not describe the interior area of a circle.