Tank

In the middle of a cylindrical tank with a bottom diameter of 479 cm, there is a standing rod 34 cm above the water surface. If we bank the rod, its end reaches the water's surface just by the tank wall.

How deep is the tank?

Correct answer:

h =  826.53 cm

Step-by-step explanation:

$$\begin{gathered} D=479\text{cm} \\ d=34\text{cm} \\ {x}^2=(D/2{)}^2+(x-d{)}^2 \\ 0=(D/2{)}^2-2\cdot x\cdot d+d^2 \\ 0=(479/2{)}^2-2\cdot x\cdot 34+34^2 \\ 136x=117032.5 \\ x=\frac{117032.5}{136}=860.53308824 \\ x=860.533088 \\ h=x-d=860.5331-34=826.53\text{cm} \end{gathered}$$

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