How Much Stone?
Calculus
How would you model this? - Explore the mathematical principles and create your own unique investigation.
Introduction
How could you determine the volume of stone required to construct this bridge? Are the arches semicircular, parabolic or some other curve? Could you use calculus to determine the cross-sectional area?
Guiding Questions
- The stone arch bridge: how much stone is in it? Decide which solid shapes to decompose it into.
- Model the arch opening with a curve and find the area between arch and deck by integration.
- Multiply up to volume and estimate the bridge's mass. Could the original builders have moved that much stone?
- Vary the arch angle or span: how does the stone needed change? Find the most economical design.