Practice Surface area and volume of cuboids and cubes
A cuboid with edges a, b and c has volume abc and surface area 2(ab + ac + bc).
These formulas help you calculate storage capacity and packaging material.
Exercises with solutions
A cuboid has six rectangular faces that come in three equal pairs. The volume is V = a · b · c, that is length times width times height. The surface area is O = 2 · (ab + ac + bc). In a cube all edges are the same length.
Exercise 1
A cuboid is 5 cm long, 3 cm wide and 4 cm high. Calculate the volume.
Show solution and working
60 cm³
V = 5 cm · 3 cm · 4 cm = 60 cm³.
Exercise 2
A cube has edge length 4 cm. Calculate the volume.
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64 cm³
For a cube V = a · a · a = 4 · 4 · 4 = 64 cm³.
Exercise 3
A cube has edge length 3 cm. Calculate the surface area.
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54 cm²
One face is 3 cm · 3 cm = 9 cm². A cube has six such faces: 6 · 9 cm² = 54 cm².
Exercise 4
A cuboid is 5 cm long, 3 cm wide and 4 cm high. Calculate the surface area.
Show solution and working
94 cm²
O = 2 · (5·3 + 5·4 + 3·4) cm² = 2 · (15 + 20 + 12) cm² = 2 · 47 cm² = 94 cm².
Common mistake
Swapping volume and surface area. Volume says how much fits inside (cm³), surface area how much material you need to cover it (cm²). Counting the faces helps: six for a cuboid.
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