Sheet № 213 · Foundation + Higher · AQA · Edexcel · OCR
Surface Area of a Cuboid –
Surface area of a cuboid is one of the most common mensuration questions on GCSE Maths papers at both Foundation and Higher tiers. You need to identify the three pairs of rectangular faces, apply the formula, and adapt it for variations like open-top boxes. This guide explains the formula, walks through worked examples at both levels, and
§Key definitions
Question:
Find the surface area of a cuboid with length 8 cm, width 5 cm, and height 3 cm.
Answer:
The surface area is 158 cm².
Q1 (Foundation):
Find the surface area of a cube with side length 6 cm.
Q2 (Foundation):
A cuboid has dimensions 10 cm × 4 cm × 3 cm. Find the surface area.
Q3 (Higher):
An open-top fish tank is 60 cm long, 30 cm wide, and 35 cm tall. How much glass is needed to make the tank?
§Formulas to memorise
Surface area of a cuboid = 2(lw + lh + wh)
Surface area of an open-top cuboid = 2(lh + wh) + lw
Worked example
Find the surface area of a cuboid with length 8 cm, width 5 cm, and height 3 cm.
Working:
⚠ Common mistakes
- ✗Forgetting to multiply by 2. Each face appears twice in a cuboid — students often calculate lw + lh + wh and forget to double.
- ✗Confusing surface area with volume. Surface area is measured in cm²; volume is measured in cm³. The formulas are completely different.
- ✗Not adjusting for open-top boxes. If the top is missing, subtract one lw face from the standard formula.
✦ Exam tips
- →Write out all three pair calculations separately before adding — this earns method marks even if you make an arithmetic error.
- →When given a net, calculate the area of each face directly rather than trying to use the formula.
- →In reverse problems (given SA, find a dimension), set up the equation carefully and solve step by step.
- →Always include the correct units — cm² for area.