For this case, the first thing you should know is that density is defined as the quotient between mass and volume. d = m / v We have then for this case that the density is: d = 103 Kg / m ^ 3 The volume is given by: V = A * d Where A: area of the city d: height of the rain Also, for calculation purposes, you must know the following measure: 1Km = 1000m 1 inch = 0.0254 meters Calculating the volume we have: V = (22 * (1000/1) ^ 2) * (2 * (0.0254 / 1)) = 1117600 m ^ 3 Then, calculating the mass we have: m = d * v m = (103) * (1117600) = 115112800 Kg Equivalently m = 1.15 * 10 ^ 8 Kg answer mass of water fell on the town was 1.15 * 10 ^ 8 Kg
We want to convert everything to meters so we can calculate cubic meter volume and use the given mass information. 2 inches = 5.08 centimeters = .0508 meters. 22 square kilometers = 22,000,000 sq meters. The product of these gives the number of cubic meters of water that rained. .0508 * 22,000,000 = 1,117,600 cubic meters. Multiply by the mass to arrive at final answer. 1,117,600 m^3 * 103kg/m^3 = 115,112,800 kg 115,112,800 kg of water fell.
