Review block 4 Vocabulary base cubed power cone exponent scientific notation cylinder perfect cube sphere cube root volume Lesson 4.1 ~ Multiplication Properties of Exponents Simplify. 1. x ⁹x ³ 2. ( p ² ) ⁴ 3. ( x ² y ) ⁶ 4. ( 3m ³ ) ² 5. ( mn ³ w ² ) ( w ⁷mn ) 6. ( 7k ² x ) ( 2k ³ x ⁹ ) 7. ( 4y ⁴ ) ² ( 2y ) ³ 8. ( 5x ² w ³ ) ² ( 3w ⁵ ) ³ 9. ( 5x ² ) ² ( x ⁴ ) ² ( 3x ² ) ³ 10. A candy company is creating a new type of chocolate bar that is packaged in a cube. The length of one side of the cube is represented by c². What term represents the volume of the cube? Show all work necessary to justify your answer. Write the volume of each rectangular prism as a single term. 11. x ³ x ³ x ³ 12. p ² q ⁵ 13. 2y 6y ⁵ 3y p ³ pq 164 Block 4 ~ Review
Lesson 4.2 ~ Division Properties of Exponents Simplify. 14. x ¹⁰ x ⁴ 15. 18y ⁴ 6y ³ 16. 3 ² 17. 5b ³c ⁷ 15bc ² 18. ( 7p ⁵m ⁴ ) ⁰ 19. ( 5w ³ 2 ) ² 20. 30x ⁵ y ² 20x ⁴ y ³ 21. ( 9d ⁵ d ) ² 22. ( h ³z ⁶ n ⁰ ) ² 23. A packaging company makes boxes with a base area represented by the expression 4a ² b ³. The length of the box is represented by ab². What expression represents the width? 24. Find the missing dimension given that the volume of the prism is 24w ⁴ y ² z. Write the missing dimension in simplest form. Show all work necessary to justify your answer. Lesson 4.3 ~ Scientific Notation Write each number in scientific notation. 6y ²? w ² 25. 0.00043 26. 40,000,000 27. 850,000 28. 0.00003 29. 798 30. 0.000000953 Write each number in standard notation. 31. 8 10⁴ 32. 5.3 10 ⁵ 33. 1.95 10 ³ 34. 6.2 10⁶ 35. 9.9 10⁷ 36. 7 10 ⁸ 37. According to www.most-expensive.net, the most expensive college to attend was Sarah Lawrence University in Bronxville, New York. In 2011, it cost about $57,600 per year to attend, including room and board. Write this number in scientific notation. 38. Texas population in 2011 could be approximated as 2.48 10⁷ people. Write this number in standard notation. 39. Nelly drank 9 10⁴ milliliters of water. Peter drank 8.49 10⁵ milliliters of water. Who drank more water? Use words and/or numbers to show how you determined your answer. Block 4 ~ Review 165
40. Frankie weighed four different diamonds. List the diamonds in order from lightest to heaviest. Weight in Diamond Ounces A 2.8 10 ² B 3 10 ³ C 9 10 ⁴ D 5.7 10 ² Lesson 4.4 Applications of Scientific Notation Find each product or quotient. Write each answer in scientific and standard notation. 41. ( 2 10⁵ ) ( 3 10⁴ ) 42. 2.1 10² 7 10 ³ 43. 1.08 10 ⁴ 6 10² 7.2 10¹⁰ 44. ( 9 10³ )( 6 10 ¹ ) 45. 8 10⁴ 46. ( 4.5 10 ⁶ )( 6 10 ⁴ ) 47. The population of India in 2010 was approximately 1.2 10⁹ people. The population of Yemen was approximately 2.4 10⁷ people. How many times more people lived in India than Yemen? Write your answer in scientific and standard notation. 48. There were approximately 3.1 10⁸ people in the United States of America in 2010. The average person ate 1.2 10² pounds of potatoes that year. a. Approximately how many pounds of potatoes were eaten in the USA in 2010? b. The average potato weighs 0.3 pounds. Approximately how many potatoes did an average American eat in 2010? Lesson 4.5 ~ Exponents and Roots Solve each equation. 49. x ³ = 1331 50. 5x ² = 245 51. 2 7 = 11 52. 3x ³ + 1 = 23 53. x ⁴ + 17 = 273 54. x² x² 15 = 0.125 2 55. The area of a circle is found using the formula A = π r ² where r is the radius. A circular placemat has an area of 301.5656 square inches. What is the approximate radius of the placemat? Use 3.14 for π. Round to the nearest tenth. 56. A box in the shape of a rectangular prism has a length of x inches, a width of 0.5x inches and a height of 2x inches. The volume of the box is 1,000 cubic inches. What is the height of the box? Show all work necessary to justify your answer. 166 Block 4 ~ Review
Solve each equation. Include all answers. Round each answer to the nearest hundredth. 57. x ² = 54 58. x ³ 2 = 19 59. 12x ³ 28 = 20 60. The volume of a cube is found using the formula V = s ³ where s is the length of a side. A cube has a volume of 9,060 square feet. What is the approximate length of a side? Round to the nearest hundredth. Lesson 4.6 ~ Volume of Cylinders Find the volume of each cylinder. Use 3.14 for π. 61. 8 m 2 m 62. 14 in 32 in 63. A 20-inch tall cylindrical fish tank has a diameter of 12 inches. a. Find the volume of the fish tank. b. One fish requires 88 cubic inches of water. How many fish can safely be put in the tank? 64. A bird feeder is the shape of a cylinder. It is 30 centimeters tall and has a radius of 4 cm. How many cubic centimeters of bird seed can be put in the feeder? Find each missing measure. Use 3.14 for π. 65. V 602.88 cm³ 66. V 1,570 in³ 4 cm r h 5 in 67. A cylindrical drinking glass can hold close to 49.5 cubic inches of water. The glass is 7 inches tall. What is the diameter of the glass? Round to the nearest whole number. Lesson 4.7 ~ Volume of Cones 68. The volume of a cylinder is 75 cm³. What is the volume of a cone with a congruent base and equal height? 69. Draw a cone with a height of 3 cm and a radius of 4 cm. Find its volume. Use 3.14 for π. Block 4 ~ Review 167
70. A sand pile is in the shape of cone. The pile is 8 1_ 2 feet tall and has a diameter of 6 feet. How many cubic feet of sand is in the pile? Use 3.14 for π. 71. Jesse had a party. He filled party hats full of treats. Each hat is 9 inches tall and has a diameter of 4 inches. a. Find the volume of one hat. Use 3.14 for π. b. Seven friends came to his party. Jesse filled one hat for each friend and one for himself. What was the volume of treats he used? Find the volume of each cone. Use 3.14 for π. 72. 1 in 73. 6 in 16 cm 20 cm 74. 3 ft 5 ft 12 cm 75. A cone has a volume close to 339.12 cm³. It is 4 cm tall. Find the radius of the cone. 76. A conical candle is made of 39.25 cm³ of wax. The diameter of the candle is 5 cm. How tall is the candle? Lesson 4.8 ~ Volume of Spheres Find the volume of each sphere. Use 3.14 for π. Round to the nearest hundredth. 77. 2 ft 78. d = 24 in 79. r = 9 m 80. Russell made a giant spherical popcorn ball. Its diameter was 12 inches. Find the volume of the popcorn ball. 81. Jacklyn made a large spherical popcorn ball that had a volume close to 5,572.45 cubic inches. Find the diameter of Jacklyn s popcorn ball. 82. Jorge was playing mush ball. The ball he was using had a volume of nearly 9,198.11 cubic centimeters. What was the radius of the mush ball? 168 Block 4 ~ Review
Judy Software Project Manager CAREER FOCUS I am a project manager for a software company. I work with people at large companies who conduct business in many different countries. Part of my job is to help companies look at their current business practices and make them better. This includes using the software that my company provides and giving training and support to businesses who use it. Math is an important part of my job. Companies who do business all over the world have to pay different tax rates or percentages depending on where things were made and where they are coming from. For instance, with the NAFTA agreement, a product manufactured in Mexico out of parts made in the US may have a reduced tax rate or be tax free when it is imported back into the US. A strong understanding of math allows me to help businesses make decisions that will maximize the profit they make. The profession of designing and supporting computer software requires at least some training after high school. Sometimes training can be done at a community college or through a program but generally people in this profession get a Bachelor s degree in computer science. In my particular position I needed further training in understanding both international trade and all of the tax laws that are involved in doing business in other countries. The average salary of someone starting out in my profession is around $60,000 per year. After 5 to7 years of experience salaries can range from $75,000 to $120,000 per year or more. There are many things I enjoy about my career; my favorite part is that I get to use math and logic in every aspect of it. It is really fun to test the results of the data that our software provides and then to use that data to help companies make good business decisions. I also enjoy working with people and getting the opportunity to teach people how to use our software. Block 4 ~ Review 169