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This test consists of 5 multiple choice questions, 5 short answer questions, and 10 short essay questions.

Multiple Choice Questions

1. In what book did Archimedes give mathematicians a logical way to start any problem and an orderly way of setting things down?
(a) Ostomachion.
(b) The Sand Reckoner.
(c) Method.
(d) On Floating Bodies.

2. For which type of science were Archimedes' demonstrations of centers of gravity the foundation?
(a) Theoretical mechanics.
(b) Quantum physics.
(c) Thermodynamics.
(d) Statistical mechanics.

3. What did Marcellus' soldiers use to make noise when they entered Syracuse?
(a) Glass jars.
(b) Shouts.
(c) Bullhorns.
(d) Trumpets.

4. What does radius mean?
(a) The longest chord of a circle.
(b) Length of a circle from the center to the rim.
(c) The shortest chord of a circle.
(d) The distance around a circle.

5. When Archimedes worked with a sphere and cylinder, he figured the ratio or relationship of the cylinder to the sphere was ___________.
(a) 6/5.
(b) 3/2.
(c) 10/9.
(d) 7/6.

Short Answer Questions

1. 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?

2. What scientist do most people believe was the first to understand the laws of gravitation?

3. What part of the Mediterranean Sea did the ships of Carthage control?

4. What did Archimedes want on his tomb?

5. How do people know that some of Archimedes' writings have been lost?

Short Essay Questions

1. Where is the earth's center of gravity?

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

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

4. How do people know that some of Archimedes' writing have been lost?

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

6. What practical joke did Archimedes play on his friends in Alexandria?

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

8. How do modern scientists work with very large numbers?

9. Describe Carthage.

10. What interests mathematicians regarding Archimedes and square roots?

(see the answer keys)

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