Floating barrel

A barrel (cylindrical in shape) floats on water with its top 18 dm above the water surface. The width of the part of the barrel above the waterline is 34 dm. The length of the barrel is 12 dm.

Calculate the volume of the barrel.

Final Answer:

V =  10930.7 dm³

Step-by-step explanation:

$$\begin{gathered} d=12\text{dm} \\ v=18\text{dm} \\ a=34\text{dm} \\ {r}^2=(a/2{)}^2+(r-v{)}^2 \\ {r}^2=(a/2{)}^2+r^2-2rv+v^2 \\ 0=(a/2{)}^2-2rv+v^2 \\ 2rv=(a/2{)}^2+v^2 \\ r=\frac{v^2+(a/2{)}^2}{2\cdot v}=\frac{18^2+(34/2{)}^2}{2\cdot 18}=\frac{613}{36}\doteq 17.0278\text{dm} \\ V=\pi \cdot r^2\cdot d=3.1416\cdot 17.0278^2\cdot 12=10930.7{\text{dm}}^3 \end{gathered}$$

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