*BookRags*. (c)2019 BookRags, Inc. All rights reserved.

Name: _________________________ | Period: ___________________ |

This quiz consists of 5 multiple choice and 5 short answer questions through Heron's Formula for Triangular Area.

## Multiple Choice Questions

**1. As described by Dunham, what did Archimedes demonstrate first in his proof on pi?**
**(a)** Area of a circle is equal to that of a right triangle that has one leg equal to the circle's radius and the other leg equal to the circle's diameter. **(b)** Area of a circle is equal to that of a right triangle that has one leg equal to the circle's radius and the other leg equal to the circle's circumference. **(c)** Area of a circle is equal to that of a right triangle that has one leg equal to the circle's diameter and the other leg equal to the circle's circumference. **(d)** Area of a circle is equal to that of a right triangle that has one leg equal to the circle's hypotenuse and the other leg equal to the circle's circumference.

**2. Dunham showed that Heron's proof could also be used as which of the following?**
**(a)** A proof of Hippocrates' squared areas. **(b)** A proof of the Pythagorean Theorem. **(c)** A proof of Euclid's number theory **(d)** A proof of Archimedes' number theory.

**3. After working on pi, what did Archimedes continue with in his study of mathematics?**
**(a)** He studied the volume to surface area ratios of cubes. **(b)** He studied the relationship between ratios in triangles. **(c)** He studied the volume and surface area of spheres, cones, and cylinders. **(d)** He studied the relationship of sine to cosine.

**4. As described by Archimedes, what is always true about he diameter of the circle?**
**(a)** It's never proportional to its circumference. **(b)** It's equal to the square of the radius. **(c)** It's equal to pi. **(d)** It's always proportional to its circumference.

**5. In general, what did Euclid's number theory describe?**
**(a)** The relationship of decimals to integers. **(b)** The nature of whole numbers. **(c)** The nature of measuring geometry. **(d)** The relationship of fractions to decimals.

## Short Answer Questions

**1.** Besides being a mathematician, what else other work was Archimedes famous for?

**2.** Heron's work referred to the work of what other famous scholar?

**3.** How did Archimedes arrive at a number value for pi?

**4.** Which of the following was one of Euclid's great theorems?

**5.** Which words best describe how solid proofs were developed in Elements?

This section contains 451 words(approx. 2 pages at 300 words per page) |