Tank 28

The tank is shaped like a cuboid. The bottom is rectangular, one side of the rectangle is 40cm long, and the diagonal of this rectangle is 50cm. The height of the tank is 1.5m. We start filling the tank with water at a rate of 1 liter per second. No water flows out. Calculate a) the volume of the tank in liters, b) how many minutes it will take for the tank to be full

Correct answer:

V =  0.18 m³
t =  3 min

Step-by-step explanation:

$$\begin{gathered} a=40\text{cm} \\ u=50\text{cm} \\ h=1.5\text{m} \\ {u}^2=a^2+b^2 \\ b=\sqrt{u^2-a^2}=\sqrt{50^2-40^2}=30\text{cm} \\ {S}_1=a\cdot b=40\cdot 30=1200{\text{cm}}^2 \\ S=S_1\to {\text{m}}^2=S_1:10000{\text{m}}^2=1200:10000{\text{m}}^2=0.12{\text{m}}^2 \\ V=S\cdot h=0.12\cdot 1.5{\text{m}}^3=0.18{\text{m}}^3 \end{gathered}$$

$$\begin{gathered} Q=1\text{l/s} \\ {V}_1=V\to \text{l}=V\cdot 1000\text{l}=0.18\cdot 1000\text{l}=180\text{l} \\ {t}_1=V_1/Q=180/1=180\text{s} \\ t=t_1\to \text{min}=t_1:60\text{min}=180:60\text{min}=3\text{min}=3\text{min} \end{gathered}$$

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