Which formula gives the area of a circle in terms of radius?

• A. A=0.7854•D²
• B. A=π•R²
• C. A=D²
• D. A=2πR

Answer: (B)

The area of a circle is proportional to the square of its radius, with π as the constant: A = π × radius^2. This comes from how area accumulates in a circle; if you imagine summing up infinitesimally thin rings, each ring has area about 2πr dr, and integrating from 0 to the radius gives πr^2.

In terms of the radius, the correct formula is A = πR^2. If you know the diameter instead, you can use D = 2R and rewrite A = π(R)^2 as A = π(D/2)^2 = (π/4)D^2 ≈ 0.7854 D^2. That shows why a form using diameter exists, but it’s not the expression asked for when given the radius.

The other options correspond to different quantities: A = 2πR is the circumference, not area, and A = D^2 would omit the essential π factor entirely, giving the wrong size for the area.