Fundamentals of Physics Extended (10th Edition)

Published by Wiley
ISBN 10: 1-11823-072-8
ISBN 13: 978-1-11823-072-5

Chapter 1 - Measurement - Problems - Page 10: 26a

Answer

The total volume of water in the cloud is between $2\times10^3m^3$ to $2\times10^4m^3$

Work Step by Step

First we calculate the volume of the cloud: $V=3000m\timesπ\times(1000m)^2=9.4\times10^9m^3$ If one $cm^2$ has 50 to 500 drops of water, then one $m^2$ would have $5\times10^7$ to $5\times10^8$ drops. We then multiply that range by our volume answer to get that the whole cloud can have between $4.7\times10^{18}$ to $4.7\times10^{19}$ drops. Then we calculate the volume of a drop: $V=\frac{4}{3}π(10^{-5}m)^3=4.2\times10^{-15}m^3$ And then by multiplying this volume by our total range of drops in the cloud to get the total volume range in the cloud. $2\times10^3m^3$ to $2\times10^4m^3$
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