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How to Calculate if a Boat Will Float

Determining the floatation properties of an object depends on the density and volume of the object and the density of the fluid containing the object. There are many designs of boats, some have a shallow draft and others have a keel that runs deep into the water, but in each case the density of the boat is less than the density of water or it would sink. Boats made from wood, steel or concrete all will float in water if the shape is correct. You can calculate if a boat will float if you know the density and volume of the boat.

Things You'll Need

Scale
Meter stick
Calculator

Instructions

- 1
  Remove the boat from the water and allow it to dry. For weight measurements, you do not want any excess weight added by the presence of water on the hull of the boat.
- 2
  Determine the weight of the dry boat. Record the weight. For purposes of an example, assume the weight was 900 kg = 900,000 grams.
- 3
  Calculate the volume of the outer hull of the boat. Do this by taking measurements of the boat and using geometric formulas to find the volume of the boat. You can use estimates of the shape to find formulas for the volume. For example, assume you need to calculate the volume of a boat that has the shape of a cylinder cut in half lengthwise. The length of the boat is 12 meters and the depth of the center of the boat is 4 meter. Calculate the volume using the geometric formula of a cylinder (V = pi x r^2 x length). Since the boat is in the shape of a half cylinder, the volume of the boat is V = 1/2 (pi x r^2 x length) = 1/2 ( pi x (4 meter)^2 x 12 meter) = 1/2 ( pi x 16 x 12) = 301.6 meter^3.
- 4
  Convert the volume to ml using 1 cubic meter equals 10^6 ml. Multiply the volume in cubic meters by 10^6 to yield ml. V = 301.6 m^3 x 10^6 ml/m^3 = 301,600,000 ml.
- 5
  Calculate the density of the boat. The total weight of the boat is the weight of the hull and the air contained in the hull is in your records from the beginning of data collection. Density is equal to the mass of the object divided by the volume of the object. Continuing the example, density = mass / volume = 900 kg / 301.6 m^3 = 0.003 g/ml .
- 6
  Compare the density of the boat with the density of water. If the density of the boat is higher than the density of water then the boat will sink. If the density of the boat is less than the density of water, then the boat will float. Finishing the example, the density of water is approximately 1 g/ml and the density of the boat is 0.003 g/ml. therefore, the boat will float.

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