Bleow are the area and volume forumlae for a number of shapes.
Remember, with many exam boards, formulae will be given to you in the exam. However, you need to know how to apply the formulae and learning them (especially the simpler ones) will help you in the exam.
When using these formulae, make sure all of the lengths are in the same units!
1km = 1000m
1m = 100cm
1cm = 10mm
1 litre = 1000 cm³
1 hectare = 10 000 m²
1 kilogram = 1000g
1cm² = 100mm² (= 10mm × 10mm)
1cm³ = 1000mm³ (= 10mm × 10mm × 10mm)
Ratios of lengths, areas and volumes
Two squares A and B have side lengths 3cm and 6cm respectively. The ratio of these lengths is 3 : 6 = 1 : 2. The area of the first is 9cm and the area of the second is 36cm. The ratio of these areas is 9 : 36 (1² : 2²) . In general, if the ratio of the lengths of two corresponding sides of two similar shapes is a : b, the ratio of their areas is a² : b² . The ratio of their volumes is a³ : b³ .
Lengths have one dimension, areas have two dimensions and volumes have three. Therefore if you are asked to choose a formula for the volume of an object from a list, you will know that it is the one with three dimensions.
The first has three dimensions, since it is the product of three lengths. The second has two dimensions; the third has three dimensions; etc. 3(a² + b²)r is the third formula with three dimensions. The expanded version of this formula is 3a²r + 3b²r and 3 dimensions + 3 dimensions = 3 dimensions.