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:

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

Try another example