Surface Area Formulas
| Shape | Formula |
|---|---|
| Cube | SA = 6s² |
| Rectangular Prism | SA = 2(lw + lh + wh) |
| Sphere | SA = 4πr² |
| Cylinder | SA = 2πr(r + h) |
| Cone | SA = πr(r + l), l = √(r²+h²) |
| Square Pyramid | SA = b² + 2b × l, l = √(h²+(b/2)²) |
What is Surface Area?
Surface area is the total area of all the outer faces of a 3D object. It is measured in square units (cm², m², in², ft²). Surface area is used in manufacturing (material cost), packaging design, heat transfer calculations, painting/coating estimation, and many engineering applications.
Worked Example — Cylinder
Cylinder: radius = 5 cm, height = 12 cm
Slant/lateral area = 2π × 5 × 12 = 376.99 cm²
Two base circles = 2 × π × 5² = 157.08 cm²
Total SA = 2π × 5 × (5 + 12) = 534.07 cm²
Frequently Asked Questions
What is the difference between surface area and volume?
Surface area measures the outer 2D skin of a 3D object (in square units). Volume measures the 3D space inside the object (in cubic units). A hollow box and a solid box with the same dimensions have the same surface area but you'd only fill the hollow one.
Why does a sphere have the smallest surface area for a given volume?
The sphere is the most efficient 3D shape — among all shapes with the same volume, it has the smallest surface area. This is why soap bubbles form spheres, why cells tend toward spherical shapes, and why ball bearings are spherical (minimal friction for a given mass).
How do I find how much paint I need to cover a surface?
Calculate the surface area in m² (or ft²), then divide by the paint coverage rate (e.g., 10 m²/litre). Add 10–15% for texture, drips, and a second coat. Subtract area of windows and doors if painting walls.
What is the lateral surface area?
Lateral surface area is the area of just the sides of a 3D shape, excluding the top and bottom bases. For a cylinder it's the curved tube; for a cone it's the slanted surface excluding the circular base; for a prism it's the rectangular sides excluding the end faces.