Write the definition of each term in your own words. Then make a sketch to describe each term visually.

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1 ssignment ssignment for Lesson.1 Name Date s the Crow Flies Properties of Spheres Write the definition of each term in your own words. Then make a sketch to describe each term visually. 1. distance as the crow flies The distance as the crow flies is used to describe a straight-line distance, i.e., the shortest distance between two points. B The distance as the crow flies across the pond from point to point B is the straight-line distance between the points. 2. circle circle is the set of all points in a plane that are equidistant from a fixed point called the center. 3. sphere sphere is the set of all points in space that are equidistant from a fixed point called the center. Circle with center Sphere with center 4. radius of a sphere radius of a sphere is the distance from the center of the sphere to a point on the sphere. 5. diameter of a sphere diameter of a sphere is the distance from a point on the sphere to another point on the sphere through the center of the sphere. B Radius B C B Diameter BC. antipodes of a sphere C ntipodes of a sphere are the endpoints of any diameter of the sphere. B Points B and C are antipodes. Chapter ssignments 117

2 7. great circle great circle is a circle on the surface of a sphere that has the same center as the sphere. Great circle 8. hemisphere hemisphere is half of a sphere, or the result when the sphere is cut through its center. Hemisphere Give a real-life example of each shape. 9. circle bracelet 10. sphere basketball 11. antipodes North and South Poles 12. hemisphere mixing bowl 118 Chapter ssignments

3 ssignment ssignment for Lesson.2 Name Date rchimedes Was head of His Time! Volume of a Sphere For each question, use 3.14 for and round your answer to the nearest hundredth, if necessary. 1. The radius of a sphere is 8 centimeters. What is the volume of the sphere? V 4 3 r (3.14)(8) The volume of the sphere is about cubic centimeters. 2. The diameter of a sphere is 42.5 inches. What is the volume of the sphere? V 4 3 r (3.14) ( ) 3 40, The volume of the sphere is about 40, cubic inches. 3. The circumference of a sphere is 12.9 meters. What is the volume of the sphere? C 2 r r r V 4 3 r ( ) (3.14) ( (3.14) ) The volume of the sphere is about 3.29 cubic meters. Chapter ssignments 119

4 4. The volume of a sphere is 125 cubic feet. What is the radius of the sphere? V 4 3 r (3.14)r r r The radius of the sphere is about 3.10 feet. 5. The volume of a sphere is cubic millimeters. What is the diameter of the sphere? V 4 3 r (3.14)r r r The radius of the sphere is about 3.78 millimeters. So, the diameter is about millimeters. can holds three tennis balls, as shown in the figure for Questions through 10. The radius of each tennis ball is 3 centimeters. For each question, use 3.14 for and round your answer to the nearest hundredth, if necessary.. What is the volume of a single tennis ball? V 4 3 r3 4 3 (3.14)(3) The volume of a single tennis ball is about cubic centimeters. r cm r cm 7. What is the total volume of all three tennis balls? Total volume The total volume of all three tennis balls is about cubic centimeters. r cm 120 Chapter ssignments

5 Name Date 8. What is the height of the can? The height of the can is equal to the height of the sum of the diameters of the three balls, or 18 centimeters. 9. What is the volume of the can? V r 2 h (3.14)(3) 2 (18) 50.8 The volume of the can is about 50.8 cubic centimeters. 10. What is the volume of the empty space in the can (the volume not taken up by tennis balls)? The volume of empty space in the can is cubic centimeters. Chapter ssignments 121

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7 ssignment ssignment for Lesson.3 Name Date Surface rea Related to Our Solar System Surface rea of a Sphere For each question, use 3.14 for and round your answer to the nearest hundredth, if necessary. 1. The radius of a sphere is 11 inches. What is the surface area of the sphere? S 4 r 2 4(3.14)(11) The surface area of the sphere is about square inches. 2. The diameter of a sphere is 17.2 meters. What is the surface area of the sphere? S 4 r 2 4(3.14) ( ) The surface area of the sphere is about square meters. 3. The circumference of a sphere is centimeters. What is the surface area of the sphere? C 2 r r r S 4 r 2 4 ( ) 2 4(3.14) ( (3.14) ) The surface area of the sphere is about square centimeters. 4. The surface area of a sphere is 500 square yards. What is the radius of the sphere? S 4 r (3.14)r r 2.31 r The radius of the sphere is about.31 yards. Chapter ssignments 123

8 5. The surface area of a sphere is square feet. What is the diameter of the sphere? S 4 r (3.14)r r r The radius of the sphere is about 13.5 feet. So, the diameter is about feet.. new umbrella design was created in the shape of a hemisphere with a special plastic coating on the material to better repel water. The diameter of the umbrella is about 1 yard. Because the umbrella is still in its beginning stages, the manufacturer only wants to produce 200 of them to be sold in select markets. How much of the special plastic coating must be produced to construct these umbrellas? Each umbrella is half of a sphere. To find the amount of plastic coating needed to make each umbrella, find the surface area of a sphere with a diameter of 1 ( radius of 1 and then divide the result by 2. 2 ) S 4 r 2 4(3.14) ( 1 2 ) So, the surface area of each umbrella is 1.57 square yards. Because there 2 are 200 umbrellas, 200(1.57) 314 square yards of plastic coating must be produced. 124 Chapter ssignments

9 Name Date 7. Suppose that the manufacturer of the umbrellas in Question has decided to make a new design for golf umbrellas, which are larger than the other umbrellas. He wants to make the same number of these new umbrellas as he did of the smaller umbrellas. The new umbrellas will have the same special plastic coating as the others, but will have twice the diameter. So, the manufacturer determines that he will need twice the material he needed to produce the smaller umbrellas. Do you agree or disagree with his decision? Explain why or why not. I do not agree with the manufacturer s decision. To find the amount of plastic coating needed to make each larger umbrella, find the surface area of a sphere with a diameter of 2 (radius of 1) and then divide the result by 2. S 4 r 2 4(3.14) ( 2 2 ) So, the surface area of each larger umbrella is.28 square yards. Because 2 there are 200 umbrellas, 200(.28) 125 square yards of plastic coating must be produced. The amount of plastic coating needed for the larger umbrellas is 125 square yards, which is not twice the amount needed for the smaller umbrellas. Instead, it is 125 times the amount needed. This is because the radius is squared Chapter ssignments 125

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11 ssignment ssignment for Lesson.4 Name Date Cookies, Peanut Butter, Basketballs, and More pplications For each question, use 3.14 for p and round your answer to the nearest hundredth, if necessary. packaging company manager wants to determine the best method for packaging golf balls to sell in stores. Each golf ball has a radius of 0.85 inches. The golf balls are to be packaged so that there are in each container. 1. One type of package the manager is considering is a cardboard box. The golf balls just fit inside the box when they are stacked on top of one another in a single column. a. What are the approximate dimensions of the box? The length of the box is about 1 golf ball long, the width of the box is about 1 golf ball wide, and the height of the box is about golf balls high. Each golf ball has a diameter of inches. The length of the box is 1.7 inches, the width of the box is 1.7 inches, and the height of the box is inches. b. What is the approximate volume of the box? V lwh 1.7(1.7)(10.2) The volume of the box is about cubic inches. c. What is the amount of wasted space inside the box when it is filled with the golf balls? Volume of each golf ball: V 4 3 r3 4 3 (3.14)(0.85) cubic inches Total volume of all golf balls in box: 2.57() cubic inches The volume of the box is cubic inches and the volume of the golf balls is cubic inches, so there are cubic inches of wasted space in the box. Chapter ssignments 127

12 d. bout how much cardboard is needed to make each box? S 2lw 2wh 2lh 2(1.7)(1.7) 2(1.7)(10.2) 2(1.7)(10.2) To make each box, cubic inches of cardboard are needed. 2. nother type of package the manager is considering is a cardboard cylinder. The golf balls just fit inside the cylinder when they are arranged in a single column so that all six are stacked inside the cylinder. a. What are the approximate radius and height of the cylinder? The diameter of the cylinder is about 1 golf ball wide, and the height of the cylinder is about golf balls high. Each golf ball has a diameter of inches. So, the radius of the cylinder is about 0.85 inches and the height of the cylinder is about inches. b. What is the approximate volume of the cylinder? V r 2 h 3.14(0.85) 2 (10.2) The volume of the cylinder is cubic inches. c. What is the amount of wasted space inside the cylinder when it is filled with the golf balls? The total volume of all golf balls in the cylinder, from Question 1, is cubic inches. The volume of the cylinder is cubic inches and the volume of the golf balls is cubic inches, so there are cubic inches of wasted space in the cylinder. d. bout how much cardboard is needed to make each cylinder? S 2 r 2 2 rh 2(3.14)(0.85) 2 2(3.14)(0.85)(10.2) To make each cylinder, cubic inches of cardboard are needed. 128 Chapter ssignments

13 Name Date 3. Based on your answers to Questions 1 and 2, which type of package do you think the manager should choose? Explain your reasoning. The manager should choose the cylinder package, because it has less wasted space and less surface area, while fitting the same number of golf balls. So, he or she would need to purchase less cardboard to make the cylinder container. 4. The cardboard used to make the packages costs $0.05 per square foot. Suppose that the manager has received an order for 10,000 packages of golf balls. How much money would the manager save on cardboard if he used the packages you chose in Question 3 to fulfill the order, compared to the other type of package that he was considering? Box: The amount of cardboard needed in square inches is 10, ,400 square inches. The amount of cardboard needed in square feet is 751,400 inches 2 1 foot 1 foot square feet. 12 inches 12 inches Total cost of cardboard: $0.05 $0.90 Cylinder package: The amount of cardboard needed in square inches is 10, ,800 square inches. The amount of cardboard needed in square feet is 589,800 inches 2 1 foot 1 foot square feet. 12 inches 12 inches Total cost of cardboard: $0.05 $ By using the cylinder package, the manager would save $20.90 $ $5.11 on the order. Chapter ssignments 129

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