Floating barrel

The barrel (cylinder shape) floats on water, the top of the barrel is 8 dm above water, and the width of the surfaced barrel part is 23 dm. The barrel length is 24 dm.

Calculate the volume of the barrel.

Correct answer:

V =  11343.3 dm³

Step-by-step explanation:

$$\begin{gathered} d=24 \\ v=8 \\ a=23 \\ {r}^2=(a/2{)}^2+(r-v{)}^2 \\ {r}^2=(a/2{)}^2+r^2-2rv+v^2 \\ 0=(a/2{)}^2-2rv+v^2 \\ 2rv=(a/2{)}^2+v^2 \\ r=(v^2+(a/2{)}^2)/(2\cdot v)=(8^2+(23/2{)}^2)/(2\cdot 8)=\frac{785}{64}\doteq 12.2656 \\ V=\pi \cdot r^2\cdot d=3.1416\cdot 12.2656^2\cdot 24=11343.3{\text{dm}}^3 \end{gathered}$$

Try another example