G4GeometryFoundation & Higher

Volume & Surface Area

Volume measures the space inside a 3D solid; surface area is the total area of all its faces. The key idea for prisms is simple: volume = area of the cross-section × length.

45 min Video by Maths Genie AQA GCSE Maths

Surface AreaWatch the walkthrough, then read the notes below.

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What you'll learn

Find the volume of prisms and cylinders
Find the surface area of solids
Use the cone, sphere and pyramid formulas (Higher)
Work in cubic units

Prisms and cylinders

A $prism$ has the same cross-section all the way through, so its volume is the cross-section area times the length. A cylinder is a prism with a circular cross-section.

prism volume = cross-section \times length

The key rule for prisms.

cylinder = π r^{2} h

Circle area × height.

V = π r^{2} h = π \times 9 \times 10

= 90 π \approx 282.7

cm³.

Answer282.7 cm³

Surface area and other solids

Surface area is found by adding the areas of all the faces — for a cylinder that is two circles plus a rectangle (the curved part). On the Higher tier you also use the sphere ( $\frac{4}{3} π r^{3}$ ) and cone formulas, which are given in the exam.

Tip — Volume uses cubic units (cm³); surface area uses square units (cm²).

Remember these

cuboid = l \times w \times h

Volume of a cuboid.

cylinder = π r^{2} h

Volume of a cylinder.

sphere = \frac{4}{3} π r^{3}

Volume of a sphere (Higher).

Watch out for these

Giving volume in cm² instead of cm³.

Volume uses cubic units.

Forgetting a face when finding surface area.

Count every face — a cuboid has 6, a cylinder has 3 parts.

Key takeaways

Prism volume = cross-section area × length.
Cylinder = πr²h; cuboid = l × w × h.
Volume in cm³, surface area in cm².

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