Question

A marble cube is immersed in a cylindrical container of diameter 16cm. It is noted that after the immersion of the cube the level of the water was risen by 1cm. How long is the side of the cube?

Answer 1

Volume of displaced water: $V_{water}=\pi r^2h=8^2*1\pi=64\pi\approx201.06\;cm^3.$

Volume of the cube: $V_{cube}=a^3=V_{water}.$

Thus, the side of the cube: $a=V_{water}^{\frac{1}{3}}=201.06^{\frac{1}{3}}=5.86\;cm.$