For students and parents · O-Level E-Math
Mensuration, the Volume and Surface-Area Questions That Recur
Volume and surface area of the standard solids.
Mrs Eileen Toh
Founder & Curriculum Architect · ex-MOE · 3 min read · Updated 29 Jun 2026
Mensuration is the measurement of volume and surface area, and in O-Level it lives mostly in Paper 2, where the hard tail of the paper often sits. The formulas for the standard solids are given to you on the formula sheet, so the marks are not for memory; they are for choosing the right formula, using the right radius and height, and handling solids made of more than one shape.
The formulas that matter
For a cylinder, radius r, height h: volume pi r2 h, curved surface 2 pi r h.
For a cone, radius r, height h, slant height l: volume (1/3) pi r2 h, curved surface pi r l.
For a sphere, radius r: volume (4/3) pi r3, surface 4 pi r2.
For a pyramid: volume (1/3) x base area x height.
The two relationships worth holding: a cone is one-third of the cylinder that boxes it, and a pyramid is one-third of the prism that boxes it. That "one-third" is the same idea twice.
A worked example for each
Cylinder, r = 7, h = 10: volume = pi x 72 x 10 = 490 pi = 1539 cm^3 to the nearest whole number.
Cone, r = 3, h = 4: volume = (1/3) pi x 32 x 4 = 12 pi = 37.7 cm^3. Its slant height is √(32 + 42) = 5, so the curved surface is pi x 3 x 5 = 15 pi = 47.1 cm^2. Note the slant height, not the vertical height, goes into the curved-surface formula; mixing the two is the standard error.
Sphere, r = 6: volume = (4/3) pi x 63 = 288 pi = 905 cm^3; surface = 4 pi x 62 = 144 pi = 452 cm^2.
The composite-solid rule
Real questions stack shapes: a cone on a cylinder, a hemisphere on a tank. The rule is to break the solid into named parts, compute each, then add for volume but think carefully for surface area, because internal joins are not surface. When a cone sits on a cylinder, the circle where they meet is inside the solid and belongs to neither outer surface. Counting a hidden face is the most common Paper 2 mensuration slip.
The teaching point
Mensuration marks turn on three things: choosing the formula, feeding it the correct length (slant height for a cone's curved surface, not the vertical height), and, for composite solids, adding volumes while excluding the hidden faces from surface area. None of it is memory work; the formulas are given. It is reading the solid correctly.
If your child can quote the formulas but loses marks on composite solids or the slant-height trap, that is a clear, fixable gap, and it sits in the part of Paper 2 that separates grades. GPA's Secondary Math programme works these on real E-Math papers. A short diagnostic consult will show where the reading slips.
Every volume and surface area on this page was checked independently before publishing.