What is the equation for the area of a sphere?

The story behind the answer

Careful: (4/3)πr^3 is the volume of a sphere, while the surface area is 4πr^2. The exponent is the key memory aid—areas scale with r^2, volumes with r^3. Archimedes showed that a sphere’s volume is two-thirds that of the cylinder that just encloses it (radius r, height 2r), giving V = (4/3)πr^3, and its surface area equals the cylinder’s lateral area, S = 4πr^2. Mnemonic: A for Area → r^2 (spread over a surface); V for Volume → r^3 (fills space).