How to use it
- Choose the solid.
- Enter its dimensions in one common unit.
- The volume and total surface area are calculated as you type.
Formulas
| Solid | Volume | Total surface area |
|---|---|---|
| Cube | s³ | 6s² |
| Box | l × w × h | 2(lw + lh + wh) |
| Cylinder | πr²h | 2πr(r + h) |
| Sphere | 4⁄3 πr³ | 4πr² |
| Cone | ⅓πr²h | πr² + πrs, with s = √(r² + h²) |
| Pyramid | ⅓ × l × w × h | lw + l√(h² + (w/2)²) + w√(h² + (l/2)²) |
| Hemisphere | ⅔πr³ | 3πr² |
The pyramid has a rectangular base and its apex sits straight above the centre of the base.
Worked examples
- Box 2 × 3 × 4. Volume 24, surface area 2 × (6 + 8 + 12) = 52.
- Sphere with radius 3. Volume 4⁄3 × π × 27 = 36π ≈ 113.097.
- Cone, radius 3, height 4. The slant height is 5, the volume 12π ≈ 37.70 and the surface area 24π ≈ 75.40.
Common mistakes
- Using the slant height as the height of a cone or pyramid. The volume needs the vertical height.
- Forgetting that units cube. Doubling every length makes the volume eight times larger and the surface area four times larger.