The surface area of a sphere with radius r is which expression?

• A. 4πr^2
• B. 2πr^2
• C. πr^2
• D. 4πr^3

Answer: (A)

Understanding how the surface area of a sphere scales with its size helps you see why the expression is 4πr^2. For a sphere, every point on the curved surface contributes, and after working through the geometry, the total surface area comes out to S = 4πr^2. This shows why the area depends on r squared: doubling the radius makes the surface area four times as large.

The other expressions don’t match the full sphere’s surface area. πr^2 is the area of a circle, not a sphere. 2πr^2 corresponds to the curved surface area of a hemisphere (without its base), not the entire sphere. 4πr^3 involves r cubed, which would relate to volume (the actual volume is (4/3)πr^3), not surface area.