Groundwater

A rainwater collection tank has the shape of a prism with trapezoidal cross-section, with parallel sides a = 5 m and c = 7 m, which are 4 metres apart. The depth of the tank is 3 metres. How many hectolitres of water can it hold at most if 8% of its volume is occupied by the pump and pipes?

Final Answer:

V =  662.4 hl

Step-by-step explanation:

$$\begin{gathered} a=5\text{m} \\ c=7\text{m} \\ v=4\text{m} \\ h=3\text{m} \\ {S}_1=\frac{a+c}{2}\cdot v=\frac{5+7}{2}\cdot 4=24{\text{m}}^2 \\ {V}_1=S_1\cdot h=24\cdot 3=72{\text{m}}^3 \\ r=100\%-8\%=1-\frac{8}{100}=0.92 \\ {V}_2=r\cdot V_1=0.92\cdot 72=\frac{1656}{25}=66.24{\text{m}}^3 \\ V=V_2\to \text{hl}=V_2\cdot 10\text{hl}=66.24\cdot 10\text{hl}=662.4\text{hl}=662.4\text{hl} \end{gathered}$$

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