Finding the volume of a prism


In Linking Thinking 1 we discovered how to fi nd the volume of a rectangular or cube-shaped prism. For any other regular prism we can use the same method. The volume of an object is how much space it takes up. Units of measure are usually mm3


, cm3


Capacity is the amount of a substance that a container can hold. Units of measure are usually ml (millilitres) or l (litres).


We can only fi nd the volume or capacity of 3D solids. To calculate the volume of rectangular solids or cubes we use the following formula.


Volume = length × width × height V = l × w × h


Worked example 2 Find the volume of (i) the cube and (ii) the rectangular solid.


1 cm 1 cm 1 cm Solution


Units of volume are always to the power of 3 (cubed), e.g. cm3


, m3


The above worked example showed that the volume of a cuboid is its length multiplied by its width multiplied by its height (volume = l × w × h ).


In the cuboid shown here, the area of the red-coloured end (the cross section) is width × height. Therefore, we can say that the volume of a cuboid is the area of the cross section (or face) multiplied by its length:


Volume = cross-sectional area × length Discuss and discover


A triangular-shaped coin to honour Pythagoras was released in the year 2000.


(i) The base of this coin is 45 mm and the perpendicular height is 22. 5 mm. Find the area of this coin.


(ii) The coin is 2 mm thick. If 20 of these coins were stacked fl at on top of each other, how high would they stand?


(iii) Using the information above, can you discover a way to fi nd the total volume of the stack of coins? Explain your answer.


h w l . 1 cm 8 cm 6 cm


height (h)


length (l)


width (w)


, m3 .


Section A Applying our skills


63


3 Volume, surface area and nets of 3D solids


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