Measuring Supporting Structures
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.
© 2000, by The Art Institute of Chicago. All rights reserved. Use of this program is subject to the terms below. No part of this program may be reproduced, transmitted or distributed in any form or by any means, except for personal or classroom use. All Copyright in and to the program, in whole or in part, belongs to the publisher and its licensors and is registered with the U.S. Copyright Office
