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This test consists of 15 multiple choice questions and 5 short answer questions.

Multiple Choice Questions

1. Before Archimedes, what did people use to figure the area of a circle?
(a) Octagons inside and outside the circle.
(b) Pentagons inside and outside the circle.
(c) Triangles inside and outside the circle.
(d) Squares inside and outside the circle.

2. 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 pi times the radius of the circle times the radius again.
(d) Multiply the radius times the circumference of a circle.

3. What is the solid of a square?
(a) Cone.
(b) Tetrahedron.
(c) Box.
(d) Cube.

4. What tower does not fall because its center of gravity is still over the tower's base?
(a) Eiffel Tower.
(b) The London Post Office Tower.
(c) Leaning Tower of Pisa.
(d) Galatia Tower.

5. Which of these would be a lemma?
(a) 1 + 1 = 2.
(b) a + b = 4c.
(c) 27 - x = 15.
(d) 33(y)=66.

6. What strait did Carthage control?
(a) Messina.
(b) Gibralter.
(c) Pentland.
(d) Cook.

7. How or where might other writings of Archimedes be rediscovered?
(a) On stone tablets.
(b) On papyrus rolls.
(c) In palimpsests.
(d) By translating ancient manuscripts.

8. How much larger did Archimedes believe that the universe (all the stars) was than the Greek universe?
(a) 50,000 times.
(b) 10,000 times.
(c) 100,000 times.
(d) 75,000 times.

9. What is the ratio of the area of a circle to the circle's diameter squared?
(a) 11 to 14.
(b) 3 to 8.
(c) 10 to 12.
(d) 5 to 9.

10. If two weights weigh the same, where will they balance?
(a) At two inches apart.
(b) In the center.
(c) At equal distances.
(d) At eight inches apart.

11. Who was the Roman general who waged war against Syracuse?
(a) Glabrio.
(b) Bonifacius.
(c) Aureolus.
(d) Marcellus.

12. 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) 1 1/2 times.
(b) 6 times.
(c) 2 1/2 times.
(d) 8 times.

13. How many papers did Archimedes write about arithmetic?
(a) Two.
(b) Four.
(c) Three.
(d) Five.

14. Where is the center of balance on a spoon?
(a) At the bowl of the spoon.
(b) In the center.
(c) Near the bowl of the spoon.
(d) Near the end of the spoon's handle.

15. Where did Rome capture city states?
(a) France.
(b) Greece.
(c) Egypt.
(d) Italy.

Short Answer Questions

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

2. What word means balance?

3. What does radius mean?

4. What is the circumference of a circle?

5. Who succeeded Hiero when he died?

(see the answer keys)

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