Compute the surface area of common three-dimensional solids.
Surface area is the total area covering the outside of a 3-D solid. Sphere: 4πr². Cone: base circle (πr²) plus lateral surface (πrl) where l is the slant height. Cube: 6 faces each a². Cylinder: two circles (2πr²) plus curved side (2πrh). Rectangular prism: 2(lw + lh + wh). Square pyramid: square base (a²) plus 4 triangular faces. Capsule: hemisphere ends (4πr²) plus cylindrical side (2πrh).
Sphere
SA = 4πr²
Cone
SA = πr² + πrl, l = √(r²+h²)
Cube
SA = 6a²
Cylinder
SA = 2πr² + 2πrh
Box
SA = 2(lw + lh + wh)
Square Pyramid
SA = a² + 2al, l = slant height
Capsule
SA = 2πrh + 4πr²
Lateral (or curved) surface area covers only the sides, not the top or bottom. Total surface area includes all faces. For a cylinder, the lateral area is the curved sheet 2πrh, while the total includes the two circular ends.
The slant height l is the distance from the apex to the rim along the surface. It forms the hypotenuse of a right triangle with the radius r and vertical height h: l = √(r² + h²).
Square units — the same length unit as your input, squared. If radius is in centimetres, surface area is in cm². Converting: 1 m² = 10 000 cm².