A reservoir has a surface area of 50.0 km^2 and an average depth of 40.0 m. Taking the density of water as 1.00 x 10^3 kg/m^3, what mass of water does it hold?

1. Mass follows from density and volume, since density is mass divided by volume, so mass equals density times volume. 2. The volume of the reservoir is its surface area multiplied by its average depth. 3. Convert the area first: 1 km is 10^3 m, so 1 km^2 is 10^6 m^2 and 50.0 km^2 = 5.00 x 10^7 m^2. 4. Volume = (5.00 x 10^7 m^2)(40.0 m) = 2.00 x 10^9 m^3. 5. Mass = (1.00 x 10^3 kg/m^3)(2.00 x 10^9 m^3) = 2.00 x 10^12 kg. 6. The value 2.00 x 10^9 kg is the trap for anyone who reports the volume in cubic metres and forgets to multiply by the density. 7. Answers of 2.00 x 10^6 kg and 2.00 x 10^15 kg come from squaring the kilometre conversion wrongly, either by leaving the area in km^2 or by using 10^6 m per km. _Source: OpenStax College Physics (CC BY 4.0), Ch 11 "Fluid Statics", section 11.2 Density_