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Sides, Volumes, and Surface Area of Solids

An ice cube is dropped into a glass that is roughly a right cylinder with a 8 cm diameter. The water level rises 2 mm. What is the volume of the cube? What is the length of one of the cube’s sides?

$V=\pi r^{2}h$

$\frac{2\ mm}{1}\times\frac{1\ cm}{10\ mm}=0.2\ cm$

$V=\pi r^{2}h,\ d=2r=8\ \rightarrow\ r=4\ cm$

$V=\pi (4\ cm)^{2}(0.2\ cm)=10.048\ cm^{3}$

$V=\sqrt[3]{s^{3}}=\sqrt[3]{10.048\ cm^{3}}$

$s=2.16\ cm$