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.
76
To find the volume of water beneath the given rectangle, we need to calculate:
1. The area of the rectangle:
- The length of the rectangle is 3.70 nautical miles = 3.70 * 6076 feet
- The width of the rectangle is 2.80 nautical miles = 2.80 * 6076 feet
- Multiply the length by the width to get the area of the rectangle in square feet.
2. Convert the depth from fathoms to feet:
- The depth is given as 28 fathoms
- Since 1 fathom is equal to 6 feet, multiply the depth by 6 to obtain the depth in feet.
3. Calculate the volume of water:
- Multiply the area of the rectangle by the depth in feet to get the volume of water in cubic feet.
4. Convert the volume from cubic feet to cubic meters:
- Since 1 cubic meter is equal to 35.3147 cubic feet, divide the volume in cubic feet by this conversion factor.
Let's calculate the volume of water beneath the given rectangle step-by-step:
Step 1: Calculate the area of the rectangle:
Length = 3.70 nautical miles * 6076 feet/nautical mile = 3.70 * 6076 feet
Width = 2.80 nautical miles * 6076 feet/nautical mile = 2.80 * 6076 feet
Area = Length * Width
Step 2: Convert the depth from fathoms to feet:
Depth in feet = 28 fathoms * 6 feet/fathom
Step 3: Calculate the volume of water:
Volume in cubic feet = Area * Depth in feet
Step 4: Convert the volume from cubic feet to cubic meters:
Volume in cubic meters = Volume in cubic feet / 35.3147
Now you can substitute the relevant values into the equations and calculate the final answer.