Question

The depth of the ocean is sometimes measured in fathoms (1 fathom = 6 feet). distance on the surface of the ocean is sometimes measured in nautical miles (1 nautical mile = 6076 feet). the water beneath a surface rectangle 4.40 nautical miles by 3.90 nautical miles has a depth of 20.0 fathoms. find the volume of water (in cubic meters) beneath this rectangle.

Answer 1

To solve the volume of water in units of cubic meters, we are going to convert first all units in terms of meter.

Let us say that the dimensions are:

length l = 4.40 nautical miles

width w = 3.90 nautical miles

depth h = 20 fathoms

Converting the dimensions to meters:

l = 4.40 nautical miles (6076 feet / nautical mile) (1 meter / 3.28 feet) = 8,150.73 m

w = 3.90 nautical miles (6076 feet / nautical mile) (1 meter / 3.28 feet) = 7,224.51 m

h = 20 fathoms (6 feet / fathom) (1 meter / 3.28 feet) = 36.59 m

The volume of a rectangular prism is:

V = l w h

Substituting the values:

V = (8,150.73 m) (7,224.51 m) (36.59 m)

V= 2,154,330,380 cubic meters