Horizontal watertank

We have a horizontal tank shaped like a rainwater cylinder, 3.45 m long and 1.7 m wide. Calculate how many liters of water is in first centimeters.

Correct answer:

V =  NAN l

Step-by-step explanation:

$$\begin{gathered} h=3.45\text{m} \\ D=1.7\text{m} \\ R=D/2=1.7/2=\frac{17}{20}=0.85\text{m} \\ {l}_0=1\text{cm}\to \text{m}=1:100\text{m}=0.01\text{m} \\ {r}_0=R-l_0=0.85-0.01=\frac{21}{25}=0.84\text{m} \\ {A}_0=R^2\cdot \arccos (r_0/R)=0.85^2\cdot \arccos (0.84/0.85)\doteq 0.1109{\text{m}}^2 \\ {B}_0=r_0\cdot \sqrt{2\cdot R\cdot h-h^2}=0.84\cdot \sqrt{2\cdot 0.85\cdot 3.45-3.45^2}=NAN{\text{m}}^2 \\ {V}_0=h\cdot (A_0-B_0)=3.45\cdot (0.1109-NAN)=NAN{\text{m}}^3 \\ V=V_0\to \text{l}=V_0\cdot 1000\text{l}=NAN\cdot 1000\text{l}=NAN\text{l}=NAN\text{l} \end{gathered}$$

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