Quadrilateral prism + water

We poured water up to a height of 34 cm into a container of a regular quadrilateral prism with a base edge a = 10.6 cm and a wall diagonal of 3.9 dm. We then inserted a 6 cm long cylinder with a diameter of 10 cm. How many liters of water overflowed?

Correct answer:

x =  0.0744 l

Step-by-step explanation:

$$\begin{gathered} a=10.6\text{cm} \\ s=3.9\text{dm}\to \text{cm}=3.9\cdot 10\text{cm}=39\text{cm} \\ h=34\text{cm} \\ {S}_1=a^2=10.6^2=\frac{2809}{25}=112.36{\text{cm}}^2 \\ {h}_2=\sqrt{s^2-a^2}=\sqrt{39^2-10.6^2}\doteq 37.5319\text{cm} \\ l=6\text{cm} \\ D=10\text{cm} \\ r=D/2=10/2=5\text{cm} \\ {V}_2=\pi \cdot r^2\cdot l=3.1416\cdot 5^2\cdot 6\doteq 471.2389{\text{cm}}^3 \\ {V}_1=S_1\cdot h=112.36\cdot 34=\frac{95506}{25}=3820.24{\text{cm}}^3 \\ {V}_3=S_1\cdot h_2=112.36\cdot 37.5319\doteq 4217.079{\text{cm}}^3 \\ {V}_4=V_1+V_2=3820.24+471.2389\doteq 4291.4789{\text{cm}}^3 \\ p=V_4-V_3=4291.4789-4217.079\doteq 74.3999{\text{cm}}^3 \\ x=p\to \text{l}=p:1000\text{l}=74.3999:1000\text{l}=0.074\text{l}=0.0744\text{l} \end{gathered}$$

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