Volume of Prisms

Key Facts and Exam Tips

• A prism is a solid with a constant cross-section. That means that if the solid is sliced anywhere along its length, the shape and size of the cross-section will always be the same.
  
• The cross-section can be any shape but exam questions tend to focus on familiar shapes like circles, triangles and trapezia, or simple composites of rectangles like L, T or H.
  
• A cylinder is a prism with a circular cross-section (Volume = r²h). Cubes and cuboids are prisms with square or rectangular cross-sections (Volume = l x b x h).
  
• The formula 'Volume = area of cross-section x length' is used to calculate the volume of any prism. First, identify the cross-section, then find its area and multiply this by the length of the prism. Sometimes the prism may be standing upright so that the 'length' is actually a height, but this makes no difference to the calculation.
  
• You will need to know the formulae for finding the area of a triangle (1/2 base x height), the area of a circle (A = r²) and the area of a trapezium (1/2 the sum of the parallel sides x the distance between them), or use the formulae given on your formulae sheet. Show the examiner clearly which formula you have used for each stage of your working.
  
• If the cross-section is a composite shape, you will need to split it into shapes whose area can be calculated. Make sure you mark clearly on the diagram how you have divided the shape up. Include the calculations for each part in your working and show how you have found the total area as this may gain method marks, even if your overall answer is wrong.
  
• The units for volume are cubed, eg cm³, m³, cubic feet and so on. You need to be particularly careful when converting between these. For example, 1m = 100cm but 1m³ = 1 000 000cm³. Always make sure that all dimensions are in the same units before you perform a calculation. Check what units are required in the answer and if necessary do a conversion.
  
• Round your answer only at the end of the final calculation, giving the degree of accuracy stated in the question (eg 3 significant figures or 1 decimal place).
  
• Capacity is a measure of the amount of liquid that will fill a space. In the metric system this is measured in litres and millilitres. To convert from cubic centimetres to litres, remember that 1 litre = 1000cm³. For cubic metres 1m³ = 1000L and for millilitres 1ml = 1cm³. (The imperial system uses fluid ounces, pints and gallons, but you won't need to convert these to volumes in your exam.)
  
• Some volume questions include working with density. Remember:
  Density = mass/volume and the units are kg/m³ or g/cm³.