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

Multiple Choice Questions

1. What is always the same as the area of a circle if one side was the same as the radius of the circle?
(a) The area of a right triangle.
(b) The area of an acute triangle.
(c) The area of an obtuse triangle.
(d) The area of an isosceles triangle.

2. Where was Carthage located?
(a) Off the coast of Spain.
(b) Near Turkey.
(c) Near Egypt.
(d) On the coast of Africa.

3. How many galleys did the Roman general have who attacked Syracuse?
(a) 60.
(b) 70.
(c) 50.
(d) 40.

4. When did Hiero die?
(a) 220 B.C.
(b) 217 B.C.
(c) 215 B.C.
(d) 212 B.C.

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

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

7. What festival was a favorite of the people in Syracuse?
(a) Festival of the Vine Flower.
(b) Greater Dionysia.
(c) Feast to Diana.
(d) Hieros Gamos.

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

9. 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.

10. When did people first glimpse the idea of gravity and its effects?
(a) 12th century.
(b) Some time during the 200s B.C.
(c) Some time during the 600s B.C.
(d) 17th century.

11. After Archimedes used a common Greek measure to estimate the number of grains of sand in the universe, what measure did he use?
(a) Cubit.
(b) Royal Cubit.
(c) Stadium.
(d) Fingerbreadths.

12. How many different sciences did Archimedes begin?
(a) Three.
(b) One.
(c) Two.
(d) Four.

13. How did Marcellus feel when he watched his soldiers conquer Syracuse?
(a) Proud.
(b) Delighted.
(c) Frustrated.
(d) Sad.

14. How did Marcellus' soldiers enter Syracuse?
(a) Through a hole in a wall.
(b) Over the wall.
(c) Through an unguarded gate.
(d) Under the wall.

15. In how many books that Archimedes sent to his friends, did he make deliberate errors?
(a) Three.
(b) One.
(c) Four.
(d) Two.

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 larger would the surface of the cylinder be than the surface of the sphere?

2. What tower does not fall because its center of gravity is still over the tower's base?

3. What calculation today does not use the unusual mathematical properties of a spiral?

4. What is a name of a paper that Archimedes wrote about arithmetic?

5. When did Marcellus notice a poorly guarded wall and tower in Syracuse?

(see the answer keys)

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