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

**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.** Which of these is not a plane figure that Archimedes discovered a method for finding the center of gravity?

**4.** What is a lemma?

**5.** What would be the area of a circle that had a radius of 3 inches?

## Short Essay Questions

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

**2.** What is the center of gravity?

**3.** Why is Archimedes' "Method" so important to all mathematicians who followed him?

**4.** Why is it possible for a person to balance standing on one foot?

**5.** What were the people of Syracuse doing when the Romans crept into their city?

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

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

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

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

**10.** Describe Marcellus' fleet that he sent to attack Syracuse.

## Essay Topics

Write an essay for ONE of the following topics:

### Essay Topic 1

Compare and contrast life in Archimedes' time to life today.

### Essay Topic 2

Discuss what life was like for Archimedes growing up.

### Essay Topic 3

Archimedes thought about and experimented with equilibrium and centers of gravity. Discuss centers of gravity and what Archimedes learned about the subject.

This section contains 771 words(approx. 3 pages at 300 words per page) |