Teach GCSE Maths Volume of a Cuboid and Isometric Drawing

Teach GCSE Maths Volume of a Cuboid and Isometric Drawing © Christine Crisp "Certain images and/or photos on this presentation are the copyrighted property of JupiterImages and are being used with permission under license. These images and/or photos may not be copied or downloaded without permission from JupiterImages"

A line has 1 dimension, length ( but we have to ignore its thickness! ) A flat surface has 2 dimensions, length and width. 4 cm 7 cm 3 cm This is a 2 -D rectangle:

Solid objects are 3-D but we draw them on a 2-D rectangle! We can use isometric paper to help us draw a 3-D object. The volume of a solid is the amount of space it takes up. Volume is measured in cubic units. e.g. cm 3, m 3, mm 3 1 cm This cube has a volume of 1 cm 3 All cubes have 6 faces, face 12 edges edge The dots are 1 cm apart. vertex and 8 vertices. Edges we cannot see are often shown as dotted lines.

This cube is made up of small cubes. 4 cm

This cube is made up of small cubes. Each of the small cubes measures 1 cm by 1 cm by 1 cm. If we look at the plan view ( from the top ), we can see the number of cubes in each layer. How many cubes are there in each layer? How many cubes altogether? Ans: There are 4  4 = 16 cubes in each layer. There are 4 layers, so there are 4  16 = 64 altogether. The volume is 64 cm 3 4 cm Plan view

Counting cubes is not a practical way of finding volume. The volume of a cube can be found by multiplying: volume = 4  4  4 = 64 cm 3 For this cube, We find the volume of a cuboid in the same way. 4 cm Plan view 4 cm Volume = length  width  height

e.g.1 Find the volume of the cuboid in the diagram. volume = 6  4  3 = 72 cm 3 Volume = length  width  height Solution: 4 cm 6 cm 3 cm We can draw a cuboid without using isometric paper.

e.g.2 Find the volume of a cuboid measuring 2 m by 1 m by 50 cm. Decide with your partner which units you would use. Solution: We must make all the units the same, either metres or centimetres. Using centimetres: Volume = length  width  height volume = 200  100  50 = cm 3 Using metres: volume = 2  1  = 1 m cm 3 = 1 m 3 So, ( 1 m = 100 cm ) ( 50 cm = ½ m ) ½ 1m1m 2m2m 50 cm

We know 100 cm = 1 m cm 3 = 1 m 3 Tell your partner why are there so many cm 3 in 1 m 3. The diagram shows us the reason. When we change from metres to centimetres, each of the measurements is multiplied by 100. To change from m 3 to cm 3 we multiply by 100  100  m1m 2m2m ½m½m 100c m 200c m 50 cm

We know that Volume = length  width  height So, if we are given the volume, length and width, we can find the height.

We know that Volume = length  width  height So, if we are given the volume, length and width, we can find the height. The easiest way is to find the area of the base. Then, Height = Volume ÷ Area of the Base So, Volume = area  height

Solution: 5 m5 m 2 m2 m h Volume = 30 m 3 e.g. Find the height, h, of the cuboid shown. Area of the base = 2  5 = 10 m 2 Height = Volume ÷ Area of the Base So, height = 30 ÷ 10 = 3 m If we are given the area of the base instead of the length and width, we have less work to do !

SUMMARY  Volume is measured in cubic units such as cm 3, m 3 and mm 3.  When we find volume, the units must all be the same. Units: 1 m = 100 cm 1 cm = 10 mm  To change from m 3 to cm 3 we multiply by 100  100  100. ( centimetres are smaller so we have more of them )  To change from cm 3 to m 3 we divide by 100  100  100.  For a cuboid, Height = volume ÷ area of the base Volume = length  width  height

EXERCISE 1. Find the volumes of the following solids: Solutions: (a) Volume = 3  3  3 Volume = length  width  height Reminder: We can write this as 3 3. = 27 cm 3 (b) Volume = 5  4  3 = 60 cm 3 Here we must write cm 3 NOT cm (a) Cube (b) Cuboid 5 cm 4 cm 3 cm

EXERCISE 2. Find the height of the cuboid with length 9 cm, width 7 cm and volume 189 cm 3 : Solution: = 189 ÷ 63 = 3 cm Height = volume ÷ area of the base Area of base = 9  7 = 63 cm 3 9 cm 7 cm h