Horizontal Cylindrical Segment

How much fuel is in the horizontal cylindrical segment tank with a length of 10m, the width of level 1 meter, and the level is 0.2 meters below the tank's upper side?

Correct answer:

V =  15.1379 m³

Step-by-step explanation:

$$\begin{gathered} a=10 \\ s=1 \\ h=0.2 \\ {r}^2=(s/2{)}^2+(r-h{)}^2 \\ {r}^2=0.25+(r-0.2{)}^2 \\ r=0.725 \\ H=2\cdot r-h=2\cdot 0.725-0.2=\frac{5}{4}=1.25 \\ A=r^2\cdot \arccos ((r-h)/r)=0.725^2\cdot \arccos ((0.725-0.2)/0.725)\doteq 0.4 \\ B=(r-h)\cdot \sqrt{2\cdot r\cdot h-h^2}=(0.725-0.2)\cdot \sqrt{2\cdot 0.725\cdot 0.2-0.2^2}=\frac{21}{80}=0.2625 \\ {S}_1=A-B=0.4-0.2625\doteq 0.1375 \\ {S}_2=\pi \cdot r^2=3.1416\cdot 0.725^2\doteq 1.6513 \\ S=S_2-S_1=1.6513-0.1375\doteq 1.5138 \\ V=S\cdot a=1.5138\cdot 10=15.1379{\text{m}}^3 \end{gathered}$$

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