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?

Result

a =  36.905 cm

Solution:

r=40 cm h=10 cm  V=π r2 h=3.1416 402 1050265.4825 cm3  V=a3  a=V3=50265.4825336.905436.905 cmr=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 } \doteq 36.9054 \doteq 36.905 \ \text{cm}



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