Studying Fossils
Estimating the Live Mass of Dinosaurs
Authors:Tim Culp and Harry J. Wolf
Woodrow Wilson Biology Institute
1995
Target age or ability group:
 High school 
Class time required:
 One period.

Materials and equipment:
 Different plastic models of dinosaurs (must be marked with scale, available through most biological supply companies)
Different plastic models of modern animals (optional)
Large beakers, jars, or small buckets OR displacement buckets
Graduated cylinders
Marking pens
Calculator (optional)

Summary of activity:
 This activity provides the student with a relatively straightforward method of estimating the live mass of the dinosaurs. It provides for an integration of math and science, requires simple measurements, includes controls, and requires logical thinking.
During the lab the student will select several different dinosaurs and modern animals (optional) to use for calculations. To save on the number of models required, we recommend that the teacher provide a couple of each type and then circulate the models during the period. The student will use a simple displacement method to calculate the volume of the model in mL (cm^{3}). This volume is then multiplied by the cube of the model's scale (to account for three dimensions) to calculate the volume of the actual animal. Once the volume of the actual animal is calculated this number can be multiplied by the density of flesh of the animal to yield the estimated mass of the actual animal. Most animals have an overall density close to the density of water. We would therefore recommend using 1 g/cm^{3} as the density of the live animal although some authors suggest a lower density of 0.85 g/cm^{3}.
After the masses of the animals are obtained using the displacement method and calculations just described, the calculated masses of the modern animal could be compared to the known masses of the actual animals. This comparison offers the student the opportunity to estimate how close the dinosaur calculations may be to the actual masses of these extinct beasts.

Prior knowledge, concepts or vocabulary necessary to complete activity: None.
 Students should be familiar with how to use the displacement method to measure volume.
Students should understand the relationship between volume, mass, and density.

Teacher Instructions
1. For the minimum amount of error with our method, it is important that the plastic models of the animals have a density greater than that of water; they should sink rather than float. The Carnegie Museum and the Natural History Museum in London each produce a line of dense plastic models which work well for this activity. A nice feature of these models is that they come with a tag giving the actual weight of the animals according to experts. This information can be withheld from your students until they have calculated their own estimated masses for the animals. These models are available in nature stores, toy stores, museums, and science supply houses.
2.Make sure the models you buy are marked with the scale. Most use a 1:40 ratio.
3. If you have displacement pans, portions of our procedure (part A) can be amended. We would recommend that glycerin or soap be added to the water in the displacement pans in order to reduce the surface tension of the water.
4. If your students are using beakers, jars, or pails rather than displacement pans, it is important that they use the narrowest container possible for each model. This will help to reduce error.
5. Rather than use the "cookbook" lab on the following page, you may wish your students to develop their own procedure given parameters which you provide them.
How Big Were the Dinosaurs?
Purpose:In this activity you will use a simple method to calculate the estimated mass of several dinosaurs. If you are careful in following the directions, your numbers will probably be close to the actual masses, since your calculations are only estimations. Only when you see the masses of these beasts can you appreciate their greatness.
Materials:Scale models of various types of dinosaurs
Large beakers, jars, or pans into which the dinosaur models can be completely submerged
Graduated cylinder
Marking pen
Models of modern animals (optional)
Procedure:
Part A
1.Obtain a model of a dinosaur. Record the type of dinosaur you are using and the scale of the model. Using the narrowest container possible, completely submerge the model in water. The container should NOT be completely filled to the brim. If the model cannot be completely submerged, you must use a larger container.
2.After the surface of the water becomes still, use the marker and carefully place a mark on the container to indicate the water line.
3.Without spilling the water, slowly retrieve the model and allow the excess water to drip from your hand and the model back into the container.
4.Notice that the water line has dropped. The volume of the model in mL (or cm^{3}.) can now be found by taking a graduated cylinder and using it to add new water to the container until the water line returns to the mark. It is critical that you record how much water it requires to bring the water line up to its previous level. This measurement is equal to the volume of the model. Record the volume of the model in cm^{3}. on the data table provided.
5.Repeat steps #14 for other models as directed by your teacher.
Part B
6.Using the volumes of the models you have collected, it is now possible to calculate the volumes of the actual animals. Before we do this it is important to review how volume is calculated. Since volume is measured in THREE dimensions, to calculate it you must multiply in three dimensions, i.e., length x width x height (L x W x H). On the model you will find the scale to which the model was produced. Since most models are produced using a 1:40 scale, we will assume those dimensions for our sample calculation below. To find the volume of the actual dinosaur, multiply the volume of your model in cm^{3}. (measured by displacement of water) by the cube of the scale. For instance, if the model has a volume of 20 cm^{3}. we multiply this number by 40 x 40 x 40 (40^{3}.) to account for the scale in all three dimensions. For our example below (see sample calculation #1), the volume of the actual animal would be 1,280,000 cm^{3}.
Sample Calculation #1
Volume of the Model

x

Scale^{3}

=

Volume of Actual Animal

e.g. 20 cm^{3}

x

40^{3}

=

1,280,000 cm^{3}

Calculate the volume for the actual animals by multiplying the model volume by the scale cubed. Record your values for each animal on the
data table.
7.The final step in calculating the mass of the animal is to multiply the volume of the actual animal by the density of the animal. Since we cannot know with certainty the density of the dinosaurs, we must make another assumption. It seems safe to assume that their density was similar to the density of living animals. Most modern animals have a density very close to the density of water (1 g/cm^{3}). When you multiply your calculated volume of the actual animal by the density of the animal (assume 1 g/cm^{3}) the units for volume cancel out, leaving youwith the mass in grams. (See sample calculation #2 below). Record this mass in the data table.
To make the mass of the animal more manageable, convert the mass in grams to kilograms by dividing the mass in grams by 1000 (see sample calculation #3 below). Calculate and record the mass in kilograms for each animal in the data table.
Sample calculations #2 and 3
Volume of Actual Animal( cm^{3})

x

Density (g/cm^{3})

=

Mass of Actual Animal (g)

e.g.1,280,000 cm^{3}

x

1 g/cm 3

=

1,280,000 g

Mass of Animal in grams (g)

x

1 kg/1000 g

=

Mass in kilograms (kg)

e.g. 1,280,000 g

x

1 kg/1000 g

=

1,280 kg

Animal Name/Scale 
Volume of Model  Volume of Animal
 Mass of Animal (g) 
Mass of Animal (kg) 
  
 
  
 
  
 
  
 
  
 
  
 
  
 
  
 
Questions
1. What were some assumptions you had to make in order to use this method?
2. What are some sources of error?
3. Considering that every model contains some error, would your calculations be closer to reality if you used a large model or a smaller model? Explain.
4. Why can't you use the mass of the model to estimate the mass of the actual animal? That is, why use the volume to get the mass?
5. What are some controls that were used in this experiment?
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