Cube into cylinder

If we dip a wooden cube into a barrel with a 40cm radius, the water will rise 10 cm. What is the size of the cube edge?

Correct answer:

a =  36.9054 cm

Step-by-step explanation:

$$\begin{gathered} r=40\text{ cm } \\ h=10\text{ cm } \\ V=\pi \cdot r^2\cdot h=3.1416\cdot 40^2\cdot 10\doteq 50265.4825{\text{cm}}^3 \\ V=a^3 \\ a=\sqrt[3]{V}=\sqrt[3]{50265.4825}=36.9054\text{ cm} \end{gathered}$$

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