### Mensuration 3 (Volume of a Cuboid)

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In addition to the demos/free presentations in this area there are at
2D
Volume of a Cuboid
Remember: the area
of a shape is a
2
measure of the
1 cm 1 cm
surface/space
1 cm
contained within its
perimeter.
3D
The volume of a
shape is a measure
1 cm 1 cm3
of the space
1 cm contained within its
1 cm
faces/boundary.
Units of area
Units of volume
mm2
mm3
Front face
cm2
m2
km2
inches2
feet2
yards2
miles2
4 cm
20 cm2
5 cm
cm3
m3
km3
inches3
feet3
yards3
miles3
2D
3D
Volume
Volume
of a Cuboid
Remember: the area
of a shape is a
2
measure of the
1 cm 1 cm
surface/space
1 cm
contained within its
perimeter.
The volume of a
shape is a measure
1 cm 1 cm3
of the space
1 cm contained within its
1 cm
faces/boundary.
Units of area
Units of volume
mm2
mm3
cm2
cm3
m2
km2
4 cm
20 cm33
40
60 cm
cm3
inches2
feet2
yards2
miles2
5 cm
m3
km3
3cm
Volume = 4 cm x 5 cm x 3 cm = 60 cm3
inches3
feet3
yards3
miles3
Volume of Cuboids
Volume = 4 mm x 3 mm x 3 mm
= 36 mm3
4 mm 36 mm3
3 mm
3 mm
2 cm
36 mm3
Volume l x w x h
Volume = 2 cm x 7 cm x 6 cm
= 84 cm3
84 cm3
84 cm3
6 cm
7 cm
Volume = 9 ft x 4 ft x 6 ft = 216 ft3
216 ft3
4 ft
? yards3
9 ft
216 ft3
6 ft
Volume of a Cuboid
Find the volume of the following cuboids.
Diagrams not to
scale.
1
4m
2m
8m
Volume = 2 x 8 x 4 = 64 m3
2
3
5 cm
5 cm
2 cm
3 cm
Volume = 2 x 3 x 5 = 30 cm3
5 cm
5 cm
Volume = 5 x 5 x 5 = 125 cm3
Volume of a Cuboid
Diagrams not to
scale.
Find the volume of the following cuboids (to 1 dp)
1
5 mm
2.3 mm
9.6 mm
2
Volume = 2.3 x 9.6 x 5 = 110.4 mm3
3
1.3 cm
3.1 cm
3.1 cm
8.1 cm
3.1 cm
12 cm
Volume = 1.3 x 12 x 8.1 = 126.4 cm3
Volume = 3.1 x 3.1 x 3.1 = 29.8 cm3
Volume of Objects
Volume = 3 cm x 13 cm x 21 cm = 819 cm3
6 cm
6 cm
6 cm
Volume = 63 = 216 cm3
3 cm
21 cm
13 cm
1.1 m
1.3 m
1.8 m
Volume = 1.3 m x 1.8 m x 1.1m = 2.574m3
Volume of Compound Shapes
Volume = 5 x 2 x 8= 80 cm3
8 cm
5 cm
8 cm
Not to
scale
512
80 cm3
cm3
288 cm3
8 cm
Volume = 83 = 512 cm3
2 cm
3 cm
12 cm
Volume = 12 x 3 x 8= 288 cm3
Volume = 512 + 288 + 80 = 880 cm3
Whiteboardmaths.com
Stand SW 100
4 10 24
16
32
6
18
8 14 9
64
7 2
1 5