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.

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