Volume of prisms

1
Volume of prisms

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

2
Volume of a prism

• You already know the volume of a cuboid

height
width
length
Volume length x width x height
3
Volume of a prism

• 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
4
Volume of a prism

• 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
5
Volume of a prism

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

Height h
Radius r
Area of cross-section pr2
Volume of prism area of cross-section x height
Volume of cylinder pr2h
6
Find the volume of a cylinder with radius 10 cm
and height 20 cm
Area of cross-section pr2 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 pr2h 314 x 20
6,280 cm3
7
Find the volume of this prism
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
8
Find the volume of this prism
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