Which expression correctly gives the area of a circle?

Which expression correctly gives the area of a circle?

• A. A = 2πr
• B. A = πd
• C. A = 4πr
• D. A = πr^2

Answer: (D)

Area of a circle is found by multiplying π by the radius squared. That makes the expression πr^2 the correct one for area, because area grows with the square of the radius. The other expressions describe the circle’s boundary, not its interior. 2πr is the circumference—the distance around the circle. If you use diameter, πd simplifies to 2πr, which again gives the circumference. The form 4πr would produce a length, not an area, and doesn’t match how area relates to the circle’s size. So πr^2 is the expression that corresponds to area.

Area of a circle is found by multiplying π by the radius squared. That makes the expression πr^2 the correct one for area, because area grows with the square of the radius.

The other expressions describe the circle’s boundary, not its interior. 2πr is the circumference—the distance around the circle. If you use diameter, πd simplifies to 2πr, which again gives the circumference. The form 4πr would produce a length, not an area, and doesn’t match how area relates to the circle’s size. So πr^2 is the expression that corresponds to area.