Volume of 2004

1-D, 2-D and 3-D shapes A straight line is one dimensional (1-D). It has only length. Units mm, cm, m & km etc. A rectangle and a circle are two dimensional (2-D) shapes. They have area. Units mm 2, cm 2, m 2 etc. A cube and a football are three dimensional (3-D) objects, They have volume (or capacity). Units mm 3, cm 3, m 3, litres etc. length

The Volume of a Prism A prism is a 3-D shape which has the same cross-section throughout its height.The following shapes are all prisms: Cuboid Triangular prism Pentagonal prism Volume of a prism = area of cross-section x vertical height

Formulae for Spheres and Cylinders r Surface Area = 4πr 2 4πr 3 3 Volume of A sphere = A cylinder is also a prism Therefore = area of cross-section x vertical height

Example Volume of a prism = area of cross-section x depth 18cm 2 10cm

CUBOID example 5cm 8cm 20cm

Example 6cm 5cm 10cm Find the Volume of this triangular prism.

Example 6cm 5cm 10cm Area of cross section = ½ x base x height = ½ x 5 x 6 = ½ x 30 = 15cm 2 Volume of a prism = Area of cross sectionx depth Volume of a prism = 15 x 10 = 150cm 3 Find the Volume of this triangular prism.

Area = 20m 2 8m A = 36m 2 5m A = 14m 2 10m A = 12m 2 15m 12m 8m 2m 4m 10m 3m A = 15m 2 11m 5m 4m 10m 3m 6m 10m 1) 2) 3) 4) 5) 6) 7) 8) 9)

Plenary! 20cm 3cm 2cm 7cm

3cm 2cm 7cm

3cm 2cm 7cm 20cm