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 3.70 nautical miles by 2.80 nautical miles has a depth of 28.0 fathoms. Find the volume of water (in cubic meters) beneath this rectangle.
Please help, I know I have conversion factor. but I just cant get the right result.
show work
1ft=.3048m
1cubic ft= (.3048)^3 meters^3
so in meters cubed, the volume=
3.70*6076ft * 2.8*6076ft * 26*6ft * (.3076)^3 m^3/ft^3
To find the volume of water beneath the surface rectangle, we need to convert the given measurements to the same unit and then use the formula for volume.
First, let's convert the dimensions of the rectangle from nautical miles to feet since the depth is given in fathoms and 1 fathom is equal to 6 feet.
3.70 nautical miles * 6076 feet/nautical mile = 22,508.2 feet
2.80 nautical miles * 6076 feet/nautical mile = 17,004.8 feet
Now, let's calculate the volume in cubic feet using the formula for the volume of a rectangular prism: Volume = Length * Width * Height.
Volume = 22,508.2 feet * 17,004.8 feet * 28.0 fathoms
However, we need to convert the volume from cubic feet to cubic meters since we want the answer in cubic meters. The conversion factor from cubic feet to cubic meters is 0.0283168 cubic meters/foot³.
To convert the volume from cubic feet to cubic meters, we multiply by the conversion factor:
Volume = (22,508.2 feet * 17,004.8 feet * 28.0 fathoms) * (0.0283168 cubic meters/foot³)
Now, let's calculate the volume by plugging in the numbers:
Volume = (22,508.2 * 17,004.8 * 28.0 * 0.0283168) cubic meters
Evaluating the expression will give you the volume of water beneath the surface rectangle in cubic meters.