How to Remember Volume Formulas
There are only three patterns behind almost every volume formula. Learn the patterns and you will not need to memorise a long list.
Rule 1: straight shapes = base × height
- Cuboid: base l × w, so V = lwh.
- Cube: base a², so V = a³.
- Cylinder: base πr², so V = πr²h.
- Any prism: V = area of the end × length.
Rule 2: pointed shapes = one third
- Cone: ⅓ of a cylinder, V = ⅓πr²h.
- Square pyramid: ⅓ of a cuboid, V = ⅓a²h.
Rule 3: round shapes have r³
- Sphere: V = ⁴⁄₃πr³.
- Hemisphere: half of that, V = ⅔πr³.
A memory trick
“Point? Divide by three. Ball? Four-thirds pi r cubed.” Say it out loud a few times before your test.
Common mistake to avoid
Using the slant height for a cone or pyramid. Volume always uses the vertical height.
Quick reference
3D Solids
Cylinder
A cylinder has two parallel circular bases joined by a curved surface. Unrolled, the curved surface is a rectangle 2πr wide.
- Volume
- V = πr2h
- Curved surface area
- CSA = 2πrh
- Total surface area
- TSA = 2πr(r + h)
- r radius
- h height
Try it yourself
Without looking: what is the volume of a cone with r = 3 and h = 10?
Show the answer
V = ⅓ × π × 9 × 10 = 30π = 94.25
Geometry Formulas Cheat SheetThe main geometry formula for every shape on a single A4 page.Download PDFOpen
Volume formulas: FAQ
What is the easiest way to remember volume formulas?
Prisms are base × height, pointed shapes are one third of that, and spheres are ⁴⁄₃πr³.
Why is a pyramid one third of a prism?
Three pyramids with the same base and height exactly fill the matching prism.
What unit is volume in?
Cubic units: cm³, m³, or litres for liquids.