Review the following concepts if needed:** **

- Fundamental Rules of Geometry for Physics Help
- Triangles for Physics Help
- Quadrilaterals for Physics Help
- Circles and Ellipses for Physics Help
- Surface Area and Volume for Physics Help

**Basics Of Geometry Practice Test**

1. A spherical particle has a volume of 8.000 × 10 ^{−9} cubic meter. What is the radius of this particle?

(a) 5.12 × 10 ^{−28} millimeter

(b) 2.000 × 10 ^{−3} millimeter

(c) 1.241 millimeters

(d) 512 millimeters

2. The earth’s radius is approximately 6,400 kilometers (km). What is the earth’s surface area in kilometers squared? Go to two significant figures. Assume that the earth is a perfect sphere.

(a) 1.28 × 10 ^{8}

(b) 5.1 × 10 ^{8}

(c) 1.1 × 10 ^{12}

(d) It cannot be calculated from this information.

3. Imagine that you have a cubical box measuring exactly 1 meter on an edge in its interior. Suppose that you are given a pile of little cubes, each measuring 1 centimeter on an edge, and told to stack the cubes neatly in the box. You are told you will receive 10 cents for each cube you stack in the box. If you complete the task, how much will you have earned?

(a) $10.00

(b) $100.00

(c) $1,000.00

(d) None of the above

4. Imagine that you are standing on the bottom of a lake whose surface is smooth, without waves. The bottom is flat and level. You shine a laser up toward the surface at an angle of 20° from the horizontal. At what angle, measured relative to the plane of the surface, will the laser beam strike the surface?

(a) 70°

(b) 35°

(c) 20°

(d) 10°

5. Suppose that you have a cylindrical container whose diameter is 10.00 centimeters and whose height is 20.00 centimeters. What is the volume of this container in centimeters cubed? Give your answer to four significant figures. Assume that π = 3.14159.

(a) 1,571

(b) 6,283

(c) 628.3

(d) 1,257

6. If the radius of a sphere is doubled, its surface area increases by a factor of

(a) 2.

(b) 4.

(c) 8.

(d) 16.

7. If the radius of an infinitely thin, flat circular disk is doubled, its surface area increases by a factor of

(a) 2.

(b) 4.

(c) 8.

(d) 16.

8. Suppose that a sample of a certain substance has a mass of 6.000 kilograms and that it is packed into a box measuring 10 centimeters wide by 20 centimeters deep by 30 centimeters high. What is the mass of 1 cubic centimeter of this substance, assuming that its density is uniform?

(a) 0.1000 gram

(b) 1.000 gram

(c) 10.00 grams

(d) 100.0 grams

9. Suppose that a light source is placed at the center of a sphere whose radius is 100 meters. If the sphere’s radius is doubled to 200 meters, what will happen to the total light energy striking the interior of the sphere?

(a) It will not change.

(b) It will be cut in half.

(c) It will become ¼ as great.

(d) There is not enough information given here to calculate it.

10. Imagine two triangles. One triangle has a base length of 3 meters, a height of 4 meters, and a slant height of 5 meters. The other triangle has a base length of 15 centimeters, a height of 20 centimeters, and a slant height of 25 centimeters. What can be said about these triangles?

(a) They are both isosceles triangles.

(b) The theorem of Pythagoras applies to both triangles.

(c) The two triangles are congruent.

(d) All of the above are true.

**Answers:**

1. c

2. b

3. d

4. c

5. a

6. b

7. b

8. b

9. a

10. b

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