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Shape and Space
Statistics and Probability
Areas and Volumes
*** 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. ***
The volume of a prism = the area of the cross-section × the length. So, for example, the volume of a cylinder = π r2 × length.
Areas (see also: shapes)
Curved surface area: 2πrh
Volume = 1/3 × area of base × perpendicular height (=1/3πr2h for circular based pyramid).
Curved surface area: πrl (l is the
"slant height", i.e. the distance from the edge of the base to the
1 kilometre (km) = 1000 m
Ratios of Lengths, Areas and Volumes
Imagine two squares, one with sides of length 3cm and one with sides of length
6cm. 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 (= 1
: 4) .
Lines 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 letters r, l, a and b represent lengths. From the following, tick the three
which represent volumes.