Depth of Water

All of the water from a full cylinder tank is drained into a rectangular aquarium. The cylinder has a height of 50 cm and a diameter of 30 cm. How deep is the water in the aquarium, if it has a rectangular base measuring 40 cm by 20 cm?

A cylinder with radius r units and height h units

has a volume of V cubic units given by 

\(\begin{array}{lcll} \boxed{~ \begin{array}{lcll} V_{\text{cylinder tank}} &=& \pi \cdot r^2 \cdot h \\ &=& \pi \cdot 30^2 \cdot 50 \ cm^3 \\ &=& 45000 \cdot \pi \ cm^3 \\ &=& 141371.669412\ cm^3 \\ \end{array} ~}\\\\ \end{array}\\\)

\(\begin{array}{lcll} \boxed{~ \begin{array}{lcll} V_{\text{aquarium}} &=& a\cdot b \cdot h \\ &=& 40\ cm \cdot 20\ cm \cdot h \\ &=& 800\ cm^2 \cdot h \\ \end{array} ~}\\\\ \end{array}\\\)

\(\begin{array}{lcll} \boxed{~ \begin{array}{lcll} V_{\text{cylinder tank}} &=& V_{\text{aquarium}} \\ 141371.669412\ cm^3 &=& 800\ cm^2 \cdot h_{\text{aquarium}} \\ h_{\text{aquarium}} &=& \frac{141371.669412\ cm^3}{800\ cm^2} \\ h_{\text{aquarium}} &=& 176.714586764\ cm \end{array} ~} \end{array}\)

The water in the aquarium is 176.7 cm deep.

Or in meters: 1.767 m

This is an ORIGINAL VOLUME = FINAL VOLUME problem

Original volume  pi x d x h   =  pi x 30 x 50 =4712.39 cm^3

This is also the FINAL VOLUME (though it is in a different shape!)

40 x 20 x h  =  4712.39

h = 4712.39/ (40 x 20) =  5.89 cm deep