1. Objective: Be able to work out the volume of a prism.
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 cuboids 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 cuboids 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 = πr2
Volume of prism = area of cross-section x height
Volume of cylinder = πr2h

6. 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
Radius 10cm
Volume of prism = area of cross-section x height
Volume of cylinder = πr2h
= 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
4 cm
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
7 cm
6cm
15cm
Volume of prism = area of cross-section x height
length
Volume of prism = 42 x 15
= 630 cm3