Rukasha Maths

GCSE maths Beta

Surface area · Revision guide

Foundation · Geometry · 2 pages in the PDF

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Learning objectives

  • Add the exposed areas of a solid using its net.
  • Adapt a closed-solid calculation for an open box or a hidden join.

Key ideas

Surface area measures the exposed surfaces; use square units, not cubic units.

For a closed cuboid, count each of the three rectangular face types twice.

S=2(lw+lh+wh)S=2(lw+lh+wh)

For a closed cylinder, add two circles and the wrapped rectangle.

S=2πr2+2πrhS=2\pi r^2+2\pi rh

Omit missing faces. For a joined face, remove both touching areas from the sum of the separate solids.

Six cuboid faces grouped into opposite pairs: two 15 square centimetre faces, two 10 square centimetre faces and two 6 square centimetre faces, totalling 62 square centimetres.

Worked examples

Example 1

Find the surface area of a closed 5 cm by 3 cm by 2 cm cuboid.

S=2(5×3+5×2+3×2)S=2(5\times3+5\times2+3\times2)
S=2(15+10+6)=62S=2(15+10+6)=62
62 cm262\text{ cm}^2

Example 2

Remove the 5 cm by 3 cm top to make an open box. Find its surface area.

Subtract the missing lid once; keep the base.

Sopen=62−5×3=47S_{\text{open}}=62-5\times3=47
47 cm247\text{ cm}^2

Watch out

Count surfaces, not edges or interior space. Do not count an absent lid or a face hidden inside a join.