Question

A heavy rainstorm dumps 1.0 cm of rain on a city 7 km wide and 8 km long in a 2-h period.

part a) How many metric tons (1 metricton = 10³ kg) of water fell on the city? (1 cm3 of water has a mass of 1 gram = 10^-3 kg.)

Express your answer using one significant figure.

part b) How many gallons of water fell on the city? (1 gal = 3.785 L.)

Express your answer using one significant figure.

Answer 1

Part A.

Volume of water dumped on the city will be:

V = Volume of cuboid = length*width*height

V = L*W*H

V = 8000 m*7000 m*0.01 m

V = 5.6*10^5 m^3

Now we know that

Mass = Volume*density

density of water = 1 gm/cm^3 = 1000 kg/m^3

So,

Mass = (5.6*10^5 m^3)*(1000 kg/m^3) = 5.6*10^8 kg

In one significant figures

Mass = 6*10^8 kg = 6*10^5*10^3 kg

Mass = 6*10^5 metric tons

Part B.

We know that

Volume of water dumped = 5.6*10^5 m^3

Now since 1 gal = 3.785 L and 1 L = 10^-3 m^3

So,

Volume = (5.6*10^5 m^3)*(1 gal/3.785 L)*(1 L/10^-3 m^3)

Volume = 5.6*10^5/(3.785*10^-3) = 147952443.85 gal

Volume = 1.48*10^8 gal

Now see that your instructor has asked to give final answer in one significant figures, So

Volume = 1*10^8 gal

(Above answer is correct in sense of significant figures, but that is never a correct way to solve a problem, if we reduce 1.48 into 1, then final answer is almost 33% less than correct value)

Let me know if you've any query.