Geometry                                                                     Names____________________________________

                                                                                                                                                                                   

Tipping the Dino Scale

 

Prerequisites: volume by displacement; density formula, Fundamental Theorem of Similarity

Materials for each group: dinosaur model, ruler/tape measure, beaker or graduated cylinder, water

 

Paleontologists can determine the size of various dinosaurs by using their fossil remains.  However, many paleontologists disagree over the approximate weight of dinosaurs. In this activity, you can hypothesize or predict the weight of a dinosaur using a scale model.

 

You can predict the mass of a dinosaur if you use the density formula:

                        density (kg/liter) = .

If you find the actual volume of a dinosaur, and use the approximate density of a dinosaur (0.9 kg/liter), then you should be able to find the dinosaur's mass.  (Note: the density of a dinosaur is hypothesized to be equal to that of a reptile.)

 

Choose a dinosaur model for your group. Your task is to find the mass of your dinosaur. You should consider using the information listed below.

 

            1liter = 1000 ml            1 kg = 2.2 lbs.              1 m = 100 cm              

 

            density (kg/liter) = mass (kg) / volume (liter)                  dinosaur density = .9 kg/liter

 

Dinosaur name

Actual Length (meters)

Dinosaur name

Actual Length (meters)

Ankylosaurus

7.5

Pachycephalosaurus

4.5

Brachiosaurus

25

Parasaurolophus

9

Brontosaurus (Apatosaurus)

24

Stegosaurus

7

Dilophosaurus  

6

Styracosaurus

5.25

Euoplocephalus           

5

Triceratops

8

Iguanadon

10

Tyrannosaurus 

11.75

 

                                   

1. Measure the length (not the width, nor the height) of the dinosaur to the nearest tenth of a centimeter and record         it in the table below.  Then convert that length into meters and record it in the table below.

 

 

2. Find the length scale factor relating your dinosaur model to the actual dinosaur. Record it in the table.

 

 

3. Select a beaker or graduated cylinder large enough that the dinosaur can fit into, but not too large.

            Measure the volume of the water without the dinosaur.                          VInitial =_________ml

 

4. Place the dinosaur into the container and approximate the final volume with the dinosaur.

                                                                                                                                    Vfinal = ___________ml

 

5. The total volume of the dinosaur model through this method of displacement can be calculated by taking the             difference of the two volumes.  Calculate this difference and record it in the table below.

 

 

6. Convert the measurement in step 5 to liters and record it in the table below.

 

 

 

7. Using the Fundamental Theorem of Similarity, find the scale factor for the volume and record it in the table.

 

 

 

Length of

Model (cm)

Length of model (m)

Actual  Length (m)             

Scale Factor for Length

Volume of Model (ml)

Volume of Model (liter)

Scale Factor for Volume

 

 

   

 

 

 

 

 

 

 

8. Find the actual volume (to the nearest liter) of the dinosaur. Show your work below.

 

 

                                                                                                                                    Volume = _________ liters

 

9. Use the density formula to find the mass of the dinosaur to the nearest kilogram.  Then convert your answer in kilograms to its equivalent value in pounds. Show your work below.

 

 

                                                                                                Mass = __________kilograms= __________pounds

 

EXTRA ALGEBRA CONNECTION:

1.      Gather the actual volume and mass data from each of the other groups. In your calculator, put the actual volume data in L1 and the actual mass data in L2.

2.      Draw a scatterplot of the data with volume as the independent variable. What do you notice about the data?

 

 

 

 

3.      Find an equation to best fit the data by eyeballing and choosing two points to determine your slope and y-intercept. Write your equation in slope-intercept form.

 

 

 

 

 

4.      Interpret the real-world meaning and units of the slope and the y-intercept.

 

 

 

 

5.      How close was the density computed from the compiled class data to that of a reptile? What may have caused any error?

 

 

 

 

 

TEACHER’S NOTES FOR DINO LAB

 

1.      This lab is designed to be done in one 50-minute class period.

2.      You may want to have a rag or roll of paper towels nearby in case of water spills.

3.      Remind students that the length of a dinosaur is measured from the tip of the nose to the tip of the tail.

4.      Suggest to students that the linear scale factor be calculated as actual/model and that the scale factor for the volume is the cube of the linear factor.

5.      Students guesses should be within 500 kg of the actual mass. The actual masses can be gotten from the following internet site:  http:/dinosauricon.com/genera/index.html

Once you are in the site, click on the name of the dinosaur. Then click on measurements at the top of the page and the mass will be displayed. Usually the mass is given in tons, so you may want to convert all of these into kilograms since the density unit is kg/l. Otherwise, have students convert to tons so that you can easily check their answers.

6.      After gathering the actual volume and mass data from each group, students may need a little review on how to determine the slope and y-intercept of the eyeballed regression line. Note that the slope should be around .9kg/l (which is the density of a reptile) and the y-intercept should be around 0.