Question 0.8: Complex Unit Conversions The volcanic explosion that destroy......
Complex Unit Conversions
The volcanic explosion that destroyed the Indonesian island of Krakatau on August 27, 1883, released an estimated 4.3 cubic miles (mi³) of debris into the atmosphere and affected global weather for years. In SI units, how many cubic meters (m³) of debris were released?
STRATEGY
We are given a volume in cubic miles and need to convert to cubic meters. It’s probably simplest to convert first from mi³ to km³ and then from km³ to m³ .
BALLPARK CHECK
As in the previous Worked Example, this is a difficult problem to estimate because it requires several different conversions. Take it one step at a time: One meter is much less than 1 mile, so it takes a large number of cubic meters to equal 1 mi³ , and the answer is going to be very large. Because 1 km is about 0.6 mi, 1 km³ is about (0.6)³ = 0.2 times as large as 1 mi³ . Thus, each mi³ contains about 5 km³ , and 4.3 mi³ contains about 20 km³ . Each km³ , in turn, contains (1000 m)³ = 10^9 m³ . The volume of debris from the Krakatau explosion was therefore about 20 × 10^9 m³ , or 2 × 10^{10} m³ . The estimate agrees with the detailed solution.