Lesson plan based on Hadrian

Calculate the volume of the Pantheon’s columns and estimate changes in weight given different parameters.

Skills and Focus: Geometry, Calculation

Subject Area: Mathematics

Thematic Connection: Counting and Calculating

Grade Level: Secondary School

Time Needed: 80 minutes

Objectives

• Determine the differences in volume of columns of different heights and diameters.

Instructional Materials Needed

Story: Who Was Hadrian?

Printouts of various views of the Pantheon (found at http://harpy.uccs.edu/roman/html/pantheonslides.html)

Activity

Step 1: After watching Who Was Hadrian?, emphasize that Hadrian was not only the emperor of Rome, but also the designer of the Pantheon and other important buildings.

Step 2: Look at images and plans of the Pantheon with the class. Discuss with the students the basic two—dimensional and three—dimensional shapes used in designing the Pantheon.

Step 3: Have students calculate the volume of the columns as they now exist. Measure their sizes on an elevation plan. The formula for the volume of a column is v = r2h.

Step 4: Have students calculate what the volume of the column would be if it were 10 meters higher yet maintained the same ratio of thickness to height (Hint: Calculate the ratio of height to thickness and use it to calculate the thickness at a different height).

Problem: How much larger a piece of granite (what percentage of the original) would be needed to make these columns 10 meters higher than they are? If the granite weighed approximately 3,000 kg/m3, how much would the columns of each size weigh?

Goals

This activity meets Illinois State Goal 8: Use algebraic and analytical methods to identify and describe patterns and relationships in data, solve problems, and predict results.

This activity meets Illinois State Goal 9: Use geometric methods to analyze, categorize, and draw conclusions about points, lines, planes, and space.

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