Quantitative Skills > Teaching Resources > Activities > BotEC: Eruption Rates

# Back-of-the-Envelope Calculations: Eruption Rates

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This activity has received positive reviews in a peer review process involving five review categories. The five categories included in the process are

• Scientific Accuracy
• Alignment of Learning Goals, Activities, and Assessments
• Pedagogic Effectiveness
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#### Summary

Question

Over the last 70 million years or so, the Hawaiian Hot Spot has been pumping out lava, a total of about 775,000 km3 worth. As the Pacific Plate has moved over the hot spot, the volcanic peaks and plateaus of the Hawaiian-Emperor seamount chain have formed. If all of that lava had erupted in California, how deeply would California be buried in lava?

## Assessment

Nearly 2 km deep! California has a surface area of about 419,000 km2. If we divide the volume of lava by the surface area of California, we'll have the answer for how deep the lava would have to be—a little more than 1.8 km deep. That's almost 6000' of lava over the entire state!

## 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:Igneous and Metamorphic Petrology:Igneous Processes, Volcanology
Resource Type: Activities:Classroom Activity:Short Activity
Special Interest: Quantitative
Quantitative Skills: Estimation