Quantitative Skills > Teaching Resources > Activities > BotEC: Scale of the Himalayas

Back-of-the-Envelope Calculations: Scale of the Himalayas

Barbara Tewksbury

Hamilton College
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Summary

Question

Let's imagine a scale model of the Earth, and let's imagine that the Earth is the size of a basketball. Suppose that you wanted to build the Himalayas to scale on the surface of the basketball. How tall would you make your scale mountains?

Assessment

Answer

About 0.2 mm (less than 1/100"!). The Earth's radius is about 6,400 km (3400 miles). The summit of Mt. Everest rises 8,848 m (29,028') above sea level. Convert meters to kilometers (8.8 km), and compare the height of Everest to the radius of the Earth. The height of Everest is roughly 0.14% of the radius of the Earth. A basketball is about 120 mm in radius. If we find 0.14% of 120 mm, we should have the scale distance of the summit of Everest above the surface of our basketball. If we multiply 120 mm x .0014, we get about 0.2 mm. So, if you wanted to build the Himalayas to scale on the basketball, you would actually have a hard time making them small enough!

References and Resources

This SERC page describes the use of Back of the Envelope Calculations

A View from the Back of the Envelope (more info) : This site has a good number of easy simulations and visualizations of back of the envelope calculations.

The Back of the Envelope : This page outlines one of the essays in the book "Programming Pearls" (ISBN 0-201-65788-0). The book is written for computer science faculty and students, but this portion speaks very well to back of the envelope calculations in general.

Controlled Vocabulary Terms

Subject: Geography:Physical, Geoscience:Geology, Mathematics
Resource Type: Activities:Classroom Activity:Short Activity
Special Interest: Quantitative
Quantitative Skills: Estimation
Ready for Use: Ready to Use
Topics: Earth surface

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