Volume of prisms
- A prism has the same cross-section all the way through. Volume = area of cross-section × length.
- Cuboid: length × width × height. Cylinder: πr²h.
- A cylinder with radius 3 cm and height 10 cm has a volume of 90π = 282.7 cm³.
Surface area
- Surface area is the total area of all the faces. Sketch the net and add up the area of each face.
- Cuboid: 2(lw + lh + wh). Cylinder: 2πr² + 2πrh (two circles plus the curved surface).
- A 5 cm by 4 cm by 3 cm cuboid has a surface area of 2 × (20 + 15 + 12) = 94 cm².
Pyramids, cones and spheres
- Pyramid volume = ⅓ × base area × height. Cone volume = ⅓πr²h. Sphere volume = 4/3 πr³.
- Sphere surface area = 4πr². Curved surface area of a cone = πrl, where l is the slant height.
- These formulae are given in the exam, but you need to know how to use them.
Units and capacity
- Volume is measured in cubic units, such as cm³ and m³.
- 1 cm³ = 1 ml, and 1000 cm³ = 1 litre.
Key terms
- Prism
- A 3D shape with the same cross-section all the way through.
- Cross-section
- The shape you see when you cut straight through a solid.
- Volume
- The amount of space inside a 3D shape.
- Surface area
- The total area of all the faces of a 3D shape.
- Net
- A flat shape that folds up to make a 3D shape.
- Cylinder
- A prism with a circular cross-section.
- Slant height
- The distance from the tip of a cone down its sloping side to the edge of the base.