Volume of prisms Starter: Higher 2007 June Q11

Volume of a cuboid We can find the volume of a cuboid by multiplying the area of the base by the height. height, h length, l width, w The area of the base = length × width Volume of a cuboid = length × width × height = lwh So,

Volume of a prism The volume of a prism is found by multiplying the area of its cross-section A by its length l (or by its height if it is standing on its cross-section). V = A l A l V = A h A h or

What is the volume of this 3-D shape? Volume of shapes made from cuboids 6 cm 5 cm 3 cm 4 cm 3 cm We can think of this shape as two cuboids joined together. Volume of the green cuboid = 6 × 3 × 3 = 54 cm 3 Volume of the blue cuboid = 3 × 2 × 2 = 12 cm 3 Total volume = = 66 cm 3

Prisms A prism is a 3-D shape that has a constant cross-section along its length. For example, this hexagonal prism has the same hexagonal cross-section throughout its length. This is called a hexagonal prism because its cross- section is a hexagon.

What is the volume of this triangular prism? Volume of a prism 5 cm 4 cm 7.2 cm Area of cross-section = ½ × 5 × 4 =10 cm 2 Volume of prism = 10 × 7.2 =72 cm 3

Volume of a prism Area of cross-section = 7 × 12 – 4 × 3 =84 – 12 = Volume of prism = 72 × 5 =360 m 3 3 m 4 m 12 m 7 m 5 m 72 m 2 What is the volume of this prism?

Lesson Objective: Be able to: Calculate the volume of a prism. Grade C/B work Outcomes: Must: Identify cross section of a prism. Should: Calculate the volume of a prism. Could: Calculate the surface area of a triangular prism. Today’s Work: Exe 4D Pages 70 & 71 Higher Edexcel 2 tier