Volume of a Prism Remember: Prisms are 3 dimensional shapes that have a constant cross-sectional...
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Transcript of Volume of a Prism Remember: Prisms are 3 dimensional shapes that have a constant cross-sectional...
Volume of a PrismRemember:
Prisms are 3 dimensional shapes that have a constant cross-sectional area.
Triangular-based prism Rectangular-based prism Pentagonal-based prism
Hexagonal-based prism Octagonal-based prism Circular-based prism
Cylinder
Cuboid
Prisms
The volume of any prism is simply its: cross-sectional area x length
9 m2
100 cm2
60 mm2
2 m9 cm
3 mm
a b
c
V = 9 x 2 = 18 m3 V = 100 x 9 = 900 cm3
V = 60 x 3 = 180 mm3
DiagramsNot to scale
Find the volume of the following prisms.
9 m2
V = 9 x 5 = 45 m3
DiagramsNot to scale
8 cm2 7 mm2
5 m 4 cm10 mm
20 mm2
10 mm
30 m2
2½ m 40 cm2
3 ¼ cm
V = 8 x 4 = 32 cm3 V = 7 x 10 = 70 mm3
V = 20 x 10 = 200 mm3 V = 30 x 2½ = 75 m3 V = 40 x 3¼ = 130 cm3
1 2 3
4 5 6
Find the volume of the following prisms.DiagramsNot to scale
4.3 m2 8.2 cm25.1 m
19.3 cm
V = 4.3 x 5.1 = 21.93 m3 V = 8.2 x 19.3 = 158.26 cm3
V = 8.2 x 10.1 = 82.82 ft3 V = 0.7 x 0.4 = 0.28 yd3
8.2 ft2
10.1 ft
0.7 yd2
0.4 yd
1 2
3 4
Find the volume of the following prisms.DiagramsNot to scale In each of the following examples the cross-sectional ends have to be
calculated.
4 m 2 m
V = 4 x 1.5 x 2 = 12 m3
1.5 m 8 cm
9 cm
4 cm
8 mm
7 mm6 mm
5 mm
1 2
3
V = ½ (9 x 8) x 4 = 144 cm3
V = ½ (8 + 6) x 7 x 5 = 245 mm3
Remember: A =½ base x height
A = ½ the sum of the parallel sides x height
5cm
8 cm 8 cm
8 cm15 cm
V = ½ x 20 x 16 x 4 = 640 cm3
V = x 82 x 10 = 3.142 x 64 x 10 = 2010cm3 (nearest cm3)
4 cm
10cm
Remember:A =½ product of
diagonals
Remember:Area = r2
r
1 2
Worksheet 1
Triangular-based prism Pentagonal-based prism
Hexagonal-based prism Octagonal-based prism Circular-based prism
Volume of a Prism
Worksheet 2
a b c
1 2 3
4 5 6
Worksheet 3
1 2
34
Worksheet 4
1 2 3
4 5