IGCSE Mathematics (0580)

Surface area and volume

What this topic tests, the mistakes that cost marks, and one exam-style question worked through step by step.

Key ideas and common mistakes

To find the volume of a cuboid, multiply all three different edge lengths together.
Common mistake: Students often forget to use all three dimensions or confuse area with volume by multiplying only two.
To find the volume of a cuboid, multiply all three dimensions (length, width, and height).
Common mistake: A common mistake is to multiply only two dimensions (the base area) and forget to include the height.
To find the radius from the volume of a sphere, substitute the given value for pi and rearrange the formula, then take the cube root (not square root).
Common mistake: Forgetting to cube root or mishandling the constants leads to common errors.
To find the volume of a pyramid, use one third of the product of the base area and the vertical height.
Common mistake: A common mistake is to omit the 1/3 or use a slant height instead of the perpendicular height.
The surface area of a cuboid is found by doubling the sum of the areas of its three distinct face pairs.
Common mistake: A common mistake is to add each face area only once, missing that each face appears twice.
When finding the volume of a frustum formed by removing a smaller cone from a larger one, use similar triangles to find the missing height of the small cone, not just subtract the given frustum height from the whole cone's height.

Work out the volume of the cuboid.

Try it first, then show the working

Answer: 1260 cm^3

20 exam-style questions on Surface area and volume, each marked to the scheme.