Marbles 4

Sipho has a cylindrical tank with a radius of 8cm and a height of 10cm. The bottom of the tank is filled with marbles, and the tank is then filled with water to a height of 6,4 cm. When the marbles are removed, the water level drops to 4cm. Using the information, help Sipho calculates the water volume displaced by the marbles. Structure your solution according to Polya's problem-solving model.

Correct answer:

x =  482.5486 cm³

Step-by-step explanation:

$$\begin{gathered} r=8\text{cm} \\ h=10\text{cm} \\ {h}_1=6.4\text{cm} \\ {h}_2=4\text{cm} \\ V=\pi \cdot r^2\cdot h=3.1416\cdot 8^2\cdot 10\doteq 2010.6193{\text{cm}}^3 \\ {V}_1=\pi \cdot r^2\cdot h_1=3.1416\cdot 8^2\cdot 6.4\doteq 1286.7964{\text{cm}}^3 \\ {V}_2=\pi \cdot r^2\cdot h_2=3.1416\cdot 8^2\cdot 4\doteq 804.2477{\text{cm}}^3 \\ x=V_1-V_2=1286.7964-804.2477=482.5486{\text{cm}}^3 \end{gathered}$$

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