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This test consists of 15 multiple choice questions and 5 short answer questions.
Multiple Choice Questions
1. With Archimedes' polygons, how much more was the circumference than the diameter?
(a) 6 15/94 times.
(b) 3 10/71 times.
(c) 1 11/63 times.
(d) 2 5/84 times.
2. What mathematics is needed to figure the cattle problem?
3. What would be the area of a circle that had a radius of 2 inches?
4. When Archimedes worked with a sphere and cylinder, he figured the ratio or relationship of the cylinder to the sphere was ___________.
5. How did the people of Syracuse celebrate their favorite festival?
(a) With plays and feasts.
(b) With dancing, games, food and wine.
(c) By making sacrifices.
(d) By fasting.
6. Before Archimedes, what did people use to figure the area of a circle?
(a) Octagons inside and outside the circle.
(b) Squares inside and outside the circle.
(c) Triangles inside and outside the circle.
(d) Pentagons inside and outside the circle.
7. 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?
(a) 6 times.
(b) 1 1/2 times.
(c) 3 1/2 times.
(d) 4 times.
8. Which of these would be a lemma?
(a) a + b = 4c.
(b) 27 - x = 15.
(c) 1 + 1 = 2.
9. With Archimedes' polygons, how much less was the circumference than the diameter?
(a) 3 1/7 times.
(b) 4 1/3 times.
(c) 2 1/2 times.
(d) 5 1/8 times.
10. How many galleys did the Roman general have who attacked Syracuse?
11. How many of Hippocrates' men did Marcellus kill?
12. What is a name of a paper that Archimedes wrote about arithmetic?
(a) The Method.
(b) The Sand Reckoner.
(d) The Palimpsest.
13. 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) 2 1/2 times.
(b) 1 1/2 times.
(c) 6 times.
(d) 8 times.
14. How much larger did Archimedes believe that the universe (all the stars) was than the Greek universe?
(a) 100,000 times.
(b) 10,000 times.
(c) 75,000 times.
(d) 50,000 times.
15. How did Marcellus' soldiers enter Syracuse?
(a) Through a hole in a wall.
(b) Under the wall.
(c) Over the wall.
(d) Through an unguarded gate.
Short Answer Questions
1. What tower does not fall because its center of gravity is still over the tower's base?
2. What does radius mean?
3. What is a good project to learn about centers of gravity?
4. When did Hiero die?
5. What word means balance?
This section contains 433 words
(approx. 2 pages at 300 words per page)