Mr Barton

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Mr Bartons Maths Notes

• Shape and Space
• 6. Volume

www.mrbartonmaths.com
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6. Volume
The Beauty of the Prism Good News So long as
you know what a prism is, and you remember how to
work out the areas of those 6 shapes we talked
about in the last section (5. Area), you can do
pretty much any volume question without needing
any more formulas!... But remember your answers
are UNITS CUBED! What is a Prism? A Prism is a
3D object whose face is the exact same shape
throughout the object. A birthday cake is the
shape of a prism if it is possible to cut it in
such a way to give everyone the exact same size
piece!
prism
prism
not a prism
prism
prism
not a prism
not a prism
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Working out the Volume of a Prism So long as you
can work out the area of the repeating face of
the prism, the formula for the volume is the same
for every single one
Volume of a Prism Area of Repeating Face
x Length
Example 1 Cuboid
Area of Repeating Face
Rectangle
Area
40cm2
Area
FACE
5 cm
4 cm
Volume of Prism
8 cm
160cm3
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Example 2 Triangular Based Prism
Area of Repeating Face
Triangle
15 m
11 m
Area
FACE
5 m
6 m
Area
33m2
Volume of Prism
165m3
Note Dont think you must use every measurement
they give you. The 15m turned out to be pretty
useless to us!
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Example 3 Cylinder
3 mm
Area of Repeating Face
FACE
Circle
Area
6.2 mm
Area
28.274 mm2
Volume of Prism
Note Keep this value in your calculator and use
it for the next sum. It keeps your answer nice
and accurate!
175.3mm3 (1dp)
Note Sometimes length can mean height when
you are working out the volume of the prism. It
just depends which way the repeating face is
facing!
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Example 4 Complicated Prism
Note This is still a prism as the front face
repeats throughout the object!
Area of Repeating Face
This time its a bit more complicated as we
cannot work out the area of the face in one go.
We must first work out the area of the complete
rectangle, and then SUBTRACT the area of the
missing circle to get our answer!
7 m
1.5 m
Rectangle
Circle
FACE
Area
Area
3 m
Area
5 m
Area
35m2
Area of Repeating Face 35 - 7.068
27.931
7.068 m2
Volume of Prism
Note Try to avoid rounding in your working out
by keeping the big numbers in the calculator, and
then only round at the end!
83.8m3 (1dp)
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Working out the Volume of Pointy
Shapes Obviously, not all 3D shapes have a
repeating face. Some shapes start off with a flat
face and end up at a point. The technical name I
have given to these shapes is Pointy Shapes!
More Good News Just like prisms, there is a
general rule for working out the volume of all
shapes like these
Volume of a Pointy Shape Area of Face
x Length
3
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Example 4 Cone
50 m
Area of Face
Circle
FACE
Diameter 180m Radius 90 m
Area
180 m
Area
25,446.9 m2
Volume of Pointy Shape
Note Keep this value in your calculator and use
it for the next sum. It keeps your answer nice
and accurate!
424,115 m3 (nearest whole number)
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Example 5 Sphere
Spheres do not have a repeating face, and they do
not end in a pointy bit, so they have a rule all
to themselves, and here it is
Volume of a Sphere
r
Volume of Sphere
12 km
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• Good luck with your revision!