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Volume of prisms

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Volume of prisms

Objective: Be able to work out the volume of a prism.

- You already know the volume of a cuboid

height

width

length

Volume = length x width x height

- Instead, think of this as the area of the cross-section times the height

height

width

length

Area of cross-section= length x width

Volume of prism = area of cross-section x height

- What is the volume of a cuboid with dimensions 10 cm, 8 cm and 5 cm.

5 cm

8 cm

10 cm

Area of cross-section= 10 cm x 8 cm = 80 cm2

Volume of prism = area of cross-section x height

= 80 cm2 x 5 cm = 400 cm3

- Volume of a cylinder is the area of the cross-section times the height

Height h

Radius r

Area of cross-section= πr2

Volume of prism = area of cross-section x height

Volume of cylinder = πr2h

Area of cross-section = πr2

= 3.14 x 102

= 3.14 x 100

= 314 cm2

Height 20cm

Radius 10cm

Volume of prism = area of cross-section x height

Volume of cylinder = πr2h

= 314 x 20

= 6,280 cm3

Cross-section is a triangle

Area of cross-section = ½ x 5 x 4

= 10 cm2

4cm

5cm

14cm

Volume of prism = area of cross-section x height

length

Volume of prism = 10 x 14

= 140 cm3

Cross-section is a parallelogram

Area of cross-section = 6 x 7

= 42 cm2

7cm

6cm

15cm

Volume of prism = area of cross-section x height

length

Volume of prism = 42 x 15

= 630 cm3