St. Clare College SS
Year 9 Track 2
Mr. A. Gauci
Mathematics
Topic 22: Volume and Surface
Area
Name of Student: ____________________________
Class: ____________________
1
St. Clare College SS
Year 9 Track 2
Mr. A. Gauci
Worksheet 22.1: Volume of Compound Shapes
Learning Outcomes:
1. I will be able to work out the volume of compound shapes.
Volume of a cuboid =
Area of cross-section x height
= length x breadth (width) x height
The area of cross-section is the face that is
repeating throughout the whole shape. In case of a
cube/cuboid, any face can be the cross-section.
B
A
Face A is repeating for 11cm (we use it as height),
12cm
C
11 cm
Face B is repeating for 12cm (we use it as height),
18.5 cm
Face C is repeating for 18.5cm (we use it as height)
This means that when it comes to cube/cuboid, the order we multiply the sides
doesn’t matter.
Example 1:
To find the volume of this cuboid we can multiply 18.5 x 12 x
12cm
11 and get 1122cm3
11 cm
18.5 cm
Example 2:
For this cube we only need one side since all are the same.
6 cm
So Volume = 6 x 6 x 6 = 216cm3
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St. Clare College SS
Year 9 Track 2
Mr. A. Gauci
Exercise 1:
Find the volume of these cubes and cuboids.
29mm
36mm
64cm
123mm
11cm
14cm
A cube with sides 1.3cm
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St. Clare College SS
Year 9 Track 2
Exercise 2:
Divide these shapes into cube/cuboids and find the total volume.
5.9cm
6.3cm
2.5cm
8cm
1.7cm
14cm
6cm
12cm
4cm
18cm
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Mr. A. Gauci
St. Clare College SS
Year 9 Track 2
5
Mr. A. Gauci
St. Clare College SS
Year 9 Track 2
Mr. A. Gauci
Worksheet 22.2: Surface Area
Learning Outcomes:
1. I will be able to find the surface area of compound shapes.
Even though 3D shapes take up volume, they still have an area we can find. This is
called the surface area, which is the area of the faces around the shape.
Cubes/cuboids have 6 faces. The surface area is the total area of these 6 faces.
Example 1:
B
Looking at this cuboid again, we have to realize that there
are 3 more hidden faces. At the back there is another
A
12cm
C
11 cm
face which is the same as A. At the bottom there is the
18.5 cm
same face as B, and on the left there is the same face as C.
To find the total surface area we can find the surface area of A and multiply it by 2
and repeat this for faces B and C. One can also find the sum of the area of faces A,
B and C and multiply that by 2.
Method 1
Method 2
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St. Clare College SS
Year 9 Track 2
Mr. A. Gauci
Example 2:
When looking at this cube we must realize that there are 6 of
the same face. So what we need to do is find the area of one
face and multiply it by 6.
Exercise 3:
Find the Total Surface Area of these shapes
100 cm
70 cm
160 cm
10 mm
8.5 mm
25 mm
803 cm
500 cm
1001 cm
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7 cm
St. Clare College SS
Year 9 Track 2
Mr. A. Gauci
10 m
6m
12 m
When finding the surface area of compound shapes, we do not need to divide the shape
into different shapes but look at each face and find the dimensions needed for their
area.
Example 3:
In this shape we know we have 8 faces.
We should always label them.
8
St. Clare College SS
Year 9 Track 2
Exercise 3:
Find the surface area of these compound shapes.
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Mr. A. Gauci
St. Clare College SS
Year 9 Track 2
10
Mr. A. Gauci