Volume of prisms

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

Volume of a prism

• You already know the volume of a cuboids

length

width

height

Volume = length x width x height

Volume of a prism

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

Area of cross-section= length x width

height

Volume of prism = area of cross-section x height

lengthwidth

Volume of a prism

• What is the volume of a cuboids with dimensions 10 cm, 8 cm and 5 cm.

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

5 cm

Volume of prism = area of cross-section x height

= 80 cm2 x 5 cm = 400 cm3

10 cm8 cm

Volume of a prism

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

Area of cross-section= πr2

Height h

Volume of cylinder = πr2h

Radius r

Volume of prism = area of cross-section x height

Find the volume of a cylinder with radius 10 cm and height 20 cm

Area of cross-section = πr2

= 3.14 x 102

= 3.14 x 100

= 314 cm2

Height 20cm

Volume of cylinder = πr2h

= 314 x 20

= 6,280 cm3

Radius 10cm

Volume of prism = area of cross-section x height

Find the volume of this prism

Cross-section is a triangle

Area of cross-section = ½ x 5 x 4

= 10 cm2

4cm

5cm

Volume of prism = 10 x 14

= 140 cm3

14cm

Volume of prism = area of cross-section x heightlength

Find the volume of this prism

Cross-section is a parallelogram

Area of cross-section = 6 x 7

= 42 cm2

7cm

6cm

Volume of prism = 42 x 15

= 630 cm3

15cm

Volume of prism = area of cross-section x heightlength