Quantitative Skills > Teaching Resources > Activities > BotEC: Size of Olympus Mons

# Back-of-the-Envelope Calculations: Size of Olympus Mons

#### Summary

Question

A picture-perfect strato-volcano such as Fujiyama in Japan is what comes to mind when most people think of a volcano. Mt. Fuji is an imposing volcanic construct, rising from nearly sea level to a summit at 3,776 m (over 12,000') above sea level. The base of the volcano is about 30 km across. Let's compare Mt. Fuji with the largest volcano on Mars, Olympus Mons.

a) Olympus Mons is over 550 km across at the base and over 26 km tall. How many Mt. Fujis could you stretch in a line across the base of Olympus Mons? How many Mt. Fujis could you stack on top of one another before you reached the height of Olympus Mons?

b) Olympus Mons has a summit caldera that is 80 km across and a maximum of 3 km deep. What is the relative size of Mt. Fuji in comparison to the summit caldera of Olympus Mons?

## Assessment

a) You could line up more than 18 Mt. Fujis across the base of Olympus Mons, and you could stack nearly 7 Mt. Fujis on top of one another before you'd reach the height of Olympus Mons. That's one big volcano!

b) You could put nearly 3 Mt. Fujis in a line across the floor of the summit caldera of Olympus Mons. If one of them was sitting in the floor of the deepest pit crater, only the top 700 meters or so would stick up above the rim of the caldera!

## References and Resources

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

A View from the Back of the Envelope : 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: Geoscience:Geology, Lunar and Planetary Science
Resource Type: Activities:Classroom Activity:Short Activity
Special Interest: Quantitative
Grade Level: High School (9-12), College Lower (13-14)
Quantitative Skills: Estimation