## Physics 211, Quiz 1

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
```