The formula for the area of a circle is:

The formula for the area of a circle is:

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

Answer: (B)

The area of a circle grows with the square of its radius and uses pi as the fixed proportionality constant, giving A = π r^2. A clear way to see this is to consider a sector of angle θ (in radians); its area is (1/2) r^2 θ. If you sum all sectors around the circle, θ runs from 0 to 2π, so the total area becomes (1/2) r^2 × (2π) = π r^2. This shows why the radius is squared and pi appears as the multiplier. The other expressions mix up parts of the circle's geometry: 2πr is the circumference, not the area; πd^2 uses diameter squared instead of radius and would yield a different value; and 2r^2 omits pi and has the wrong scaling for area.

The area of a circle grows with the square of its radius and uses pi as the fixed proportionality constant, giving A = π r^2. A clear way to see this is to consider a sector of angle θ (in radians); its area is (1/2) r^2 θ. If you sum all sectors around the circle, θ runs from 0 to 2π, so the total area becomes (1/2) r^2 × (2π) = π r^2. This shows why the radius is squared and pi appears as the multiplier.

The other expressions mix up parts of the circle's geometry: 2πr is the circumference, not the area; πd^2 uses diameter squared instead of radius and would yield a different value; and 2r^2 omits pi and has the wrong scaling for area.