Volume of cuboids, prisms and cylinders, their surface areas, capacity in litres, and packing and filling problems.
What you will learn
- Find the volume of a prism as area of cross-section × length
- Find the surface area of a cuboid, prism or cylinder
- Use 1 litre = 1000 cm³
- Solve packing and filling problems
Cross-section times length
A prism has the same cross-section all the way through.
Its volume is the area of that cross-section times the length.
prism: V = area of cross-section × length
cuboid: V = length × width × height
cylinder: V = πr²h
A cylinder is a prism with a circle as its cross-section.
- triangular prism: cross-section ½ × 6 × 8 = 24 cm², length 15 cm
- V = 24 × 15 = 360 cm³
Working backwards, divide the volume by what you know. A cuboid of volume 120 cm³ that is 5 cm by 4 cm has height 120 ÷ (5 × 4) = 6 cm. A cylinder of radius 5 cm holding 2 litres (2000 cm³, since 1 litre = 1000 cm³ and 1 ml = 1 cm³) has height 2000 ÷ (π × 5²) = 25.5 cm. If you are given the diameter, halve it for the radius first.
The rest of this lesson and its 8 practice questions are locked.
In this lesson
- Cross-section times length
- Surface area is every face added
- Capacity and filling
- Try it: Spot the prisms
8 practice questions, marked as you go; about 25 minutes in all.
Key terms
Prism, Open
In this unit: Area, perimeter and volume
Perimeter and area of rectangles, triangles, parallelograms, trapeziums and compound shapes, circles, arcs and sectors, and the volume and surface area of prisms, cylinders, pyramids, cones and spheres.
- Perimeter and area
- Circles
- Arcs and sectors
- Volume and surface area of prisms
- Cones, pyramids and spheres
- Solids, nets, plans and elevations