Cylinder horizontally

The cylinder with a diameter of 3 m and a height/length of 15 m is laid horizontally. Water is poured into it, reaching a height of 60 cm below the axis of the cylinder. How many hectoliters of water is in the cylinder?

Correct answer:

V =  267.5273 hl

Step-by-step explanation:

$$\begin{gathered} D=3\text{ m } \\ R=D\mathrm{/}2=3\mathrm{/}2={\displaystyle \frac{3}{2}}=1.5\text{ m } \\ L=15\text{ m } \\ r=60\mathrm{/}100={\displaystyle \frac{3}{5}}=0.6\text{ m } \\ h=R-r=1.5-0.6={\displaystyle \frac{9}{10}}=0.9\text{ m } \\ {S}_1=R^2\cdot \arccos (r\mathrm{/}R)=1.5^2\cdot \arccos (0.6\mathrm{/}1.5)\doteq 2.6084{\text{m}}^2 \\ {S}_2=r\cdot \sqrt{2\cdot R\cdot h-h^2}=0.6\cdot \sqrt{2\cdot 1.5\cdot 0.9-0.9^2}\doteq 0.8249{\text{m}}^2 \\ S=S_1-S_2=2.6084-0.8249\doteq 1.7835{\text{m}}^2 \\ {V}_1=L\cdot S=15\cdot 1.7835\doteq 26.7527{\text{m}}^3 \\ V=V_1\to \text{ hl}=V_1\cdot 10\text{ hl}=26.7527\cdot 10\text{ hl}=267.527\text{ hl}=267.5273\text{ hl} \end{gathered}$$

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