Surface area = add up every face
For a prism, add the two ends and all the rectangular faces; for a cylinder, ; cone curved surface (slant height ).
Volume formulae
Prism cross-section area length; cylinder ; sphere ; cone ; pyramid base area height.
Drawn from real examiner reports.
Surface area: missing or doubling faces
Finding the volume by mistake, not halving the triangle area, forgetting the slant face, or forgetting one triangular end.
In examiner reports students found the volume instead of the surface area, forgot the slant face, or forgot one triangular end.
Hemisphere: halve the sphere volume
Forgetting to divide the sphere formula by 2 for a hemisphere, or using instead of .
In examiner reports students used the sphere formula instead of the hemisphere, or wrote $\tfrac43\pi r^2$ instead of $r^3$.
Wrong volume–capacity conversion
Not knowing litre (and litres); dividing by 100 or 10000.
In examiner reports many divided the volume by 100 or 10 000 instead of using 1000 cm³ = 1 litre.
Cone: slant height, not vertical height
For the curved surface use the slant height in , never the vertical height. Add the base circle only when the cone is solid or closed.
Cylinder area: keep both circles
The surface is the two ends plus the curved part: . Dropping one circle (writing ) or leaving off the curved part is a common slip.
Use brackets when substituting
Put brackets around a substituted expression (e.g. ) so the whole thing is squared.
Quote the formula, then substitute
Write the correct volume or surface-area formula, then substitute the numbers before evaluating. This secures the method mark even if the final arithmetic slips.
Check cm² against cm³
Surface area is a square unit (); volume is a cubic unit (). If your working gives the wrong power, you have used the wrong formula — re-read what is asked.
| Solid | Volume |
|---|---|
| Prism | cross-section area length |
| Cylinder | |
| Sphere | |
| Cone | |
| Pyramid | base area height |
A hemisphere is half a sphere: . (Use , not .)
Volume of a cylinder?
A cylinder has radius cm and height cm. Find its volume, correct to 1 d.p.