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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. What would be the area of a circle that had a radius of 3 inches?
(a) 12.3454.
(b) 45.33813.
(c) 5.9986.
(d) 28.27431 inches.

2. What did Marcellus have his workmen build when he noticed a poorly guarded wall and tower in Syracuse?
(a) Bridges.
(b) Climbing poles.
(c) Scaling ladders.
(d) Step ladders.

3. How many sides did the polygons have that Archimedes used to determine the area of a circle?
(a) 96.
(b) 36.
(c) 8.
(d) 112.

4. When did Marcellus notice a poorly guarded wall and tower in Syracuse?
(a) 209 B.C.
(b) 215 B.C.
(c) 225 B.C.
(d) 212 B.C.

5. What is the solid of a circle?
(a) Cone.
(b) Box.
(c) Sphere.
(d) Cube.

Short Answer Questions

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

2. How did Marcellus' soldiers enter Syracuse?

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

4. How did Marcellus feel when he watched his soldiers conquer Syracuse?

5. What is the solid of a triangle?

Short Essay Questions

1. What interests mathematicians regarding Archimedes and square roots?

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

3. What is the difference between a plane and a solid figure?

4. What did Archimedes consider to be his most important work?

5. What are some reasons why Archimedes is held in such high esteem by mathematicians?

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

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

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

9. What happened when a soldier came to bring Archimedes to Marcellus?

10. What agreement did the Romans and Carthaginians make to divide the Mediterranean between themselves?

(see the answer keys)

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