Copyright © Michael Richmond.
This work is licensed under a Creative Commons License.
Question 1:
The depth of the ocean is sometimes measured in fathoms: 1 fathom = 6 feet. Distance on the surface of the ocean is often measured in nautical miles: 1 nautical mile = 6076 feet.
One particular portion of the ocean is a rectangle 1.20 nautical miles by 2.60 nautical miles. It has a depth of 16 fathoms.
What is the volume of water beneath this area? Express your answer in cubic feet.
Answer: volume = (area on top) * (depth)
Now, the area on top is 1.2 x 2.6 nautical miles, but we need
to convert to feet:
6076 feet
1.20 nautical miles * ----------- = 7,290 feet
1 naut mile
6076 feet
2.60 nautical miles * ----------- = 15,800 feet
1 naut mile
where I've kept only 3 significant digits in the number of feet,
since there are only 3 significant digits in the number of
nautical miles.
The depth of this region is
6 feet
16 fathoms * --------- = 96 feet
fathom
So the volume of the region is
volume = (area on top) * (depth)
= (7,290 feet) * (15,800 feet) * (96 feet)
= 1.11 x 10^10 cubic feet
Copyright © Michael Richmond.
This work is licensed under a Creative Commons License.