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