volume

ntroduction Volume is a measure of the space taken up by a solid object and is measured in cubic units such as cubic centimetres (cm³) or cubic metres (m³). The Imperial system uses units such as cubic feet (ft³). A solid such as a cube or a cuboid is three-dimensional (3D). That simply means that you need three measurements in order to work out its volume, length, width and height. Sometimes the last measurement is called depth or thickness. A unit cube has six square faces, and all three dimensions are the same, 1cm. The volume of the cube is 1 cubic centimetre (1 cm³). In simple cases you can find the volume of an object by counting the number of unit cubes it contains. Each of the following diagrams represents a shape made from unit cubes. Volume and capacity are not quite the same thing; capacity is the amount a solid can contain. In the metric system capacity is usually measured in litres. (The Imperial system uses gallons). Remember: 1000 cm³ = 1000 millilitres = 1 litre. Cubes and cuboids A cuboid is a solid with six rectangular faces and all its angles right angles.(A cube is a special example of a cuboid because all its faces are squares.). Example 1 Each of these two cuboids has the same volume, 8 cm³, and the same dimensions: length 4 cm, width 2 cm, height 1 cm. The volume of the first can be found by counting the unit cubes.The volume of the second is found using the rule: Volume of a cuboid = length x width x height The dimensions of a cube are all the same, so the rule for finding the volume is: Volume of a cube = length x length x length = length³ Example 2 Its volume is 2 x 2 x 2 = 8 cm³ Practical examples The most important thing to remember when you are working out practical examples of volume or capacity is that all measurements must be in the same units. You will often have measurements in both metres and centimetres; change them all into the same units before you begin your calculation. Example 1 Vijay's window box is a cuboid of length 1 m, width 20 cm and height 30 cm. Work out its volume. Make all the units centimetres.1 m = 100 cm, so the volume is 100 x 20 x 30 = 60 000 cm³ Example 2 Igor is working out how many cubic metres of concrete he will need for his patio. It will be 2 metres wide and 8 metres long and he needs to make it 10 cm deep. How much concrete will he need? Make all the units metres.10 cm = 0.1 m, so the volume = 8 x 2 x 0.1 = 16 x 0.1 = 1.6 m³ Example 3 Bonny has made a rectangular garden pond 2 m long and 1 m wide. She wants to fill it to a depth of 30 cm. How many litres of water will she need? Make all the units centimetres. 200 x 100 x 30 = 600  000 cm³Remember that 1 litre = 1000 cm³600  000 ÷ 1  000 = 600She will need 600 litres of water. Cylinders (These examples are Level 2 of the curriculum.) Look at this box. The volume is width x height x lengthThe width x height is the area of the end.So the volume can be written      area of end x length This works for cylinders too. Cylinders This cylinder has a circular end, straight sides, and is the same width all the way along.Just like the box the volume is      area of end x length You can use this to find the volumes of cylinderical containers. Example How many litres of compost do you need to fill this plant holder? The volume is end area x length. That is      1 000 x 50 = 50 000 cm³A litre is 1 000 cm³. So the volume of the plant holder is      50 000 ÷ 1 000 = 50 litresSo you need 50 litres of compost to fill it. Follow the link below to practice sheets http://www.bbc.co.uk/skillswise/numbers/measuring/volume/worksheet.shtml