WJEC MATHEMATICS
INTERMEDIATE
SHAPE AND AREA
VOLUME
1
Contents
Volume of basic shapes
Capacity
Finding the depth
Credits
WJEC Question bank
http://www.wjec.co.uk/question-bank/question-search.html
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Volume of basic shapes
The volume of a 3D shape is the amount of space taken up by the
shape. The units will be cubic (e.g. cm3, mm3, litres, ml, etc.)
Counting cubes
The easiest way to calculate volume is to count the cube that an
object is made from.
The easiest way to count all the small cubes would be to count how
many cubes make the front face and then multiply it by two (The
shape is 2 layers deep)
Number of cubes on the front face = 47
So total cubes = 47 x 2 = 94
You may require units on your answer. If you are told each
square is 1cm3, then this answer would be 94cm3
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Volume of Prisms
A prism is a three dimensional solid with uniform cross section. (it
looks like one shape that has been stretched backwards). Here are
examples of prisms.
VOLUME = AREA OF CROSS SECTION
LENGTH
Think of this as the 'front
face'
More commonly for cuboids, we say
VOLUME = LENGTH
WIDTH
HEIGHT
Examples
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Exercise G15
Calculate the volume of the following shapes
1.
2.
3.
5
4.
5.
6
6.
7.
7
8.
9.
Capacity
Often, volume questions include units. Two important conversions
that you should know are;
Example
Find the volume of the cuboid in litres
To convert from
to ,
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Exercise G16
Find the volume of the following shapes in litres
64cm
1.
2.
5.1m
2.1m
59cm
86cm
Finding the depth
For some questions, you will be given the volume but not the depth.
For these questions, you will need to form and solve an equation.
Example
1.8 litres of water is poured into the following container. How high is
the water level?
We need to form an equation and then
solve it.
[Remember 1.8 litres = 1800cm3]
30cm
5cm
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Exercise G17
2.4 litres of water is poured into the following container. Calculate the
depth of the water.
30cm
20cm
Exam Questions G26
1.
2.
10
3.
4.
11
5.
12