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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.** Which of these would be a lemma?

**2.** If you took a sphere and made a cylinder whose base was the greatest circle of the sphere and whose height was the diameter of the sphere, how much space or volume would the cylinder take up compared to the sphere?

**3.** What did Archimedes want on his tomb?

**4.** What was the value of the largest number for which the Greeks had a name?

**5.** What books did Archimedes send to friends in Alexandria with deliberate errors?

## Short Essay Questions

**1.** How do modern scientists work with very large numbers?

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

**3.** Describe Carthage.

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

**5.** Why isn't the center of gravity always at the center of an object?

**6.** Why did Marcellus watch the battle for Syracuse with tears in his eyes?

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

**8.** How did Archimedes estimate the number of grains that would fill the universe?

**9.** What calculations did Archimedes use to show how numbers were infinite?

**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

Archimedes furthered his studies at the Museum in Alexandria. Discuss the library and Museum at Alexandria and Archimedes' studies there.

### 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

There are three different classes of levers. Discuss how a lever works and how the relationship of the different parts of a lever create the different lever classes.

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