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This test consists of 5 short answer questions, 10 short essay questions, and 1 (of 3) essay topics.

Short Answer Questions

1. When Archimedes estimated the number of grains of sand that would fill the universe, what common Greek measure did he use?

2. What did Marcellus have his workmen build when he noticed a poorly guarded wall and tower in Syracuse?

3. What did Marcellus do while Syracuse was in siege?

4. For which type of science were Archimedes' demonstrations of centers of gravity the foundation?

5. When did Marcellus notice a poorly guarded wall and tower in Syracuse?

Short Essay Questions

1. What happens when a pebble is dropped into a pond?

2. What agreement did the Romans and Carthaginians make to divide the Mediterranean between themselves?

3. What is a chain reaction in a nuclear explosion?

4. What did Archimedes set out to prove in "The Sand Reckoner"?

5. Why did Archimedes not want to help King Hiero make plans to defend Syracuse from a possible attack?

6. What is the center of gravity?

7. How do mathematicians figure the area of a circle?

8. What is the difference between a plane and a solid figure?

9. Before Archimedes, how did people find the area of a circle?

10. What happened when a soldier came to bring Archimedes to Marcellus?

Essay Topics

Write an essay for ONE of the following topics:

Essay Topic 1

King Hiero wanted Archimedes to determine if his new crown was solid gold. Discuss how Archimedes solved the crown problem using what is called today the Scientific Method.

Essay Topic 2

Archimedes wanted to be more exact than mathematicians before him when figuring the area of a circle. Discuss different methods that Archimedes, mathematicians before him, and mathematicians after him have used to find the area of a circle.

Essay Topic 3

Discuss how and why Archimedes created the Archimedean screw.

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