The area of a circle depends on which variable?

The area of a circle depends on which variable?

• A. Diameter
• B. Height
• C. Circumference
• D. Radius

Answer: (D)

The area of a circle depends on its radius because the standard formula for area is A = πr^2. The radius is the distance from the center to the edge, and the area increases with the square of that distance. For example, doubling the radius makes the area quadruple (A = π(2r)^2 = 4πr^2). That shows why radius is the defining variable for area. Diameter is directly related (it's twice the radius), so you could use diameter to get the area, but you still rely on the radius in the formula. Circumference (2πr) involves the same radius but is a different property, not the factor that appears in the area formula. Height isn’t a factor for a circle, since a circle is a flat 2D shape with no height.

The area of a circle depends on its radius because the standard formula for area is A = πr^2. The radius is the distance from the center to the edge, and the area increases with the square of that distance. For example, doubling the radius makes the area quadruple (A = π(2r)^2 = 4πr^2). That shows why radius is the defining variable for area.

Diameter is directly related (it's twice the radius), so you could use diameter to get the area, but you still rely on the radius in the formula. Circumference (2πr) involves the same radius but is a different property, not the factor that appears in the area formula. Height isn’t a factor for a circle, since a circle is a flat 2D shape with no height.