How to find surface area
- Choose the shape.
- Enter its measurements in one unit.
- Read the total surface area in square units, with the formula and the volume.
Why surface area matters
Paint, wrapping, insulation and heat loss all depend on surface area. Bigger objects have less surface for their volume: double every length and the volume grows 8 times but the surface only 4 times. That is why large animals keep warm more easily and crushed ice melts faster than a block.
Formulas
| Solid | Surface area |
|---|---|
| Cube | 6a² |
| Box | 2(lw + lh + wh) |
| Cylinder | 2πr(r + h) |
| Sphere | 4πr² |
| Hemisphere | 3πr² |
| Cone | πr(r + slant height) |
Painting and wrapping
For paint, work out the surface you’ll actually cover: a room’s walls are a box’s sides without the floor and ceiling, minus doors and windows. Divide the area by the coverage on the tin and add a second coat if needed.