The surface area of a solid is the total area of all its faces, measured in square units such as cm2. A helpful way to find it is to imagine the net and add up the area of every piece. Throughout, take π = 22/7 unless told otherwise.
Formulas to know
- Cube of side a: surface area = 6a2
- Cuboid l × w × h: 2(lw + lh + wh)
- Closed cylinder radius r, height h: 2πr2 + 2πrh = 2πr(r + h)
- Sphere radius r: 4πr2
- Cone radius r, slant height l: πr2 + πrl = πr(r + l)
Worked example
Find the surface area of a closed cylinder with r = 7 cm and h = 10 cm. Surface area = 2πr(r + h) = 2 × 22/7 × 7 × (7 + 10) = 2 × 22 × 17 = 748 cm2.
Working backwards
You can also start from a known surface area and find a length. If a cube has surface area 96 cm2, then 6a2 = 96, so a2 = 16 and a = 4 cm.
Key idea
Surface area is always in square units (cm2, m2). Add every face — do not miss the two ends of a cylinder or prism.
Remember
- Curved surface of a cylinder = 2πrh; add 2πr2 for the two circular ends.
- Curved surface of a cone = πrl (l is the slant height, not the vertical height).
- Sphere: 4πr2 — one clean formula.