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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. 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 larger would the surface of the cylinder be than the surface of the sphere?
(a) 8 times.
(b) 1 1/2 times.
(c) 2 1/2 times.
(d) 6 times.

2. What is the circumference of a circle?
(a) The ratio between the diameter and the radius.
(b) The distance from the center of a circle to the rim.
(c) The distance from rim to rim of a circle.
(d) The distance around the circle.

3. When Buffon, a French scientist, made a mirror following the description of Archimedes' mirrors, how far away could he set fire to wood?
(a) 150 feet.
(b) 100 feet.
(c) 75 feet.
(d) 50 feet.

4. What is the formula for the area of a circle?
(a) Multiply the length of the circle from rim to rim times pi.
(b) Subtract the radius from the circumference of a circle.
(c) Multiply the radius times the circumference of a circle.
(d) Multiply pi times the radius of the circle times the radius again.

5. How long was a stadium?
(a) 600 feet.
(b) 12 feet.
(c) 500 feet.
(d) 35 feet.

Short Answer Questions

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

2. Which mathematicians probably used a decimal system of numbers?

3. How did the people of Syracuse celebrate their favorite festival?

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

5. What historian wrote an account of the battle between Rome and Syracuse?

Short Essay Questions

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

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

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

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

5. Describe Marcellus' fleet that he sent to attack Syracuse.

6. How did Archimedes figure the area of a circle?

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

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

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

10. What is the center of gravity?

(see the answer keys)

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