Volume and Surface Area
8 min read · Updated September 26, 2026 · by the SolveCalcPro editorial team
Volume measures how much space a solid takes up, in cubic units. Surface area measures the total area of its outside faces, in square units. You use volume to fill things (a tank, a box) and surface area to cover them (wrap, paint).
Formulas
| Solid | Volume | Surface area |
|---|---|---|
| Cube (side s) | s³ | 6s² |
| Box (l, w, h) | lwh | 2(lw + lh + wh) |
| Cylinder (r, h) | πr²h | 2πr(r + h) |
| Cone (r, h, slant l) | ⅓πr²h | πr(r + l) |
| Sphere (r) | 4/3 πr³ | 4πr² |
Worked examples
- Cube with side 4: volume 64, surface area 96.
- Box 6 × 4 × 3: volume 72, surface area 2(24 + 18 + 12) = 108.
- Cylinder with r = 3 and h = 10: volume 90π ≈ 282.74 and surface area 78π ≈ 245.04.
- Cone with r = 3 and h = 4: the slant height is 5, volume 12π ≈ 37.70 and surface area 24π ≈ 75.40.
- Sphere with r = 5: volume 500π/3 ≈ 523.60 and surface area 100π ≈ 314.16.
Verify with the geometry calculator.
Where the ⅓ comes from
A cone holds exactly one third of the cylinder with the same base and height. The same is true of a pyramid compared with a prism.
Volume and capacity
1 m³ = 1,000 litres and 1 litre = 1,000 cm³. A tank measuring 2 m × 1 m × 1.5 m holds 3 m³, which is 3,000 litres.
Scaling
If you double every length, surface area becomes four times larger and volume eight times larger. That is why a small change in size can greatly change how much a container holds.
Practice questions
Test yourself, then tap to check. Answers are calculated by the tools linked below.
- Area of a circle with radius 7.
Show answer
Area: 153.93804
- How many kilometres is a 26.2-mile marathon?
Show answer
26.2 mi in km: 42.1648128
- A circle has diameter 14. Find its area and circumference.
Show answer
Radius: 7 · Diameter: 14 · Circumference: 43.98229715
Frequently asked questions
What is the difference between volume and surface area?
Volume is the space inside; surface area is the area of the outside.
How do I find the slant height of a cone?
Use the Pythagorean theorem: l = √(r² + h²).
Why are volumes in cubic units?
You are counting unit cubes that fill the solid.
How many litres are in a cubic metre?
1,000.
Try it yourself
Geometry CalculatorArea, perimeter, circumference, volume and surface area of common shapes.Unit ConverterConvert length, mass, temperature, volume, area and speed between metric and imperial units.Circle CalculatorFind radius, diameter, circumference and area from any one of them.Keep learning
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