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NSW Y8 Maths Volume Volume and Capacity

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Volume and Capacity Theory

\fbox{\(1 \text{~L}=1000 \text{~mL}\)} \quad \fbox{\(1 \text{KL}=1000 \text{~L} \)} \quad \fbox{\(1 \text{~mL}=1000 \text{~kL}\)} \quad \fbox{\(1 \text{~cm}^3=1 \text{~mL}\)} \quad \fbox{\(1 \text{~m}^3=1 \text{~kL} \text { or } 1000 \text{~L}\)}\\ \begin{multicols}{2} \textbf{Example 1}\\ A tank is in the shape of a rectangular prism with dimensions \(1.5 \text{~m}, 2 \text{~m}\) and \(4 \text{~m}\). How many litres of water would fill the tank?\\ \textbf{Example 1 solution}\\ \(\begin{aligned} V & =1.5 \times 2 \times 4 \\ & =12 \text{~m}^3 \\ & =12 \text{~kL} \\ & =12000 \text { Litres } \end{aligned}\) \columnbreak \textbf{Example 2}\\ Three centimetres of rain fall during the day. Determine the volume of water in kilolitres that falls on 2 hectares of ground.\\ \textbf{Example 2 solution}\\ \(\begin{aligned} 1 \text{ha} & =10000 \text{~m}^2 \\ 3 \text{~cm} & =3 \div 100 \text{~m} \\ & =\frac{3}{100} \text{~m} . \end{aligned}\)\\ \(\begin{aligned} \therefore \text { Volume } & =2 \times 10000 \times \frac{3}{100} \\ & =600 \text{~m}^3 \\ & =600 \text{~kL} . \end{aligned}\) \end{multicols}

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