Find the circumference of each circle. Round to the nearest tenth. 1. The circumference is about 125.7 kilometers. 2. The circumference is about 44.0 yards. 3. diameter = The circumference is about 16.8 feet. 4. radius = 13.5 mm The circumference is about 84.8 millimeters. esolutions Manual - Powered by Cognero Page 1
5. A Ferris wheel has a diameter of 250 feet. What is the distance, to the nearest whole foot, that riders travel if they stay on it for 15 rotations? The circumference is about 785.4 feet. If the riders stayed on for 15 rotations, they traveled 15 785.4 or about 11,781 feet. Find the area of each circle. Round to the nearest tenth. 6. The area is about 201.1 square centimeters. 7. The radius is half the diameter, so. The area is about 143.1 square inches. esolutions Manual - Powered by Cognero Page 2
8. A pie has a diameter of 9 inches. Find the area of the top crust. Round to the nearest tenth. The radius is half the diameter, so 9 2 = 4.5. The area is about 63.6 square inches. 9. Find the area of the composite figure. Find the areas of the rectangle and of the triangle. Then add. So, the area of the composite figure is 6 + 2.25 or 8.25 square inches. esolutions Manual - Powered by Cognero Page 3
10. The floor plan of a new museum is shown. What is the area of the museum rounded to the nearest whole foot? Find the area of the museum by breaking it down into simpler figures. The floor plan of the museum is made up of a square, 4 rectangles, and 4 semicircles. There are 4 rectangles, so the area of the rectangles is 4 1200 or 4800 square feet. There are 4 semicircles, so the area of the semicircles is 4 1413.7 or about 5655 square feet. So, the area of the museum is 3600 + 4800 + 5655 or about 14,055 square feet. Identify each figure. Name the bases, faces, edges, and vertices. 11. Sample answer: This figure has two rectangular bases, ADGF and BCHE, so it is a rectangular prism. faces: ABCD, EFGH, BEFA, CHGD, ADGF, BCHE edges:,,,,,,,,,,, vertices: A, B, C, D, E, F, G, H esolutions Manual - Powered by Cognero Page 4
12. 13. Sample answer: This figure has one triangular base, QRS, so it is a triangular pyramid. faces: QRT, QST, TSR, QRS edges:,,,,, vertices: Q, R, S, T 14. This figure has one square base, LMNO, so it is a square pyramid. faces: LPM, LPO, NPO, NPM, LMNO edges:,,,,,,, vertices: L, M, N, O, P This figure has one circular base, circle A, and a vertex connected by a curved side, so it is a cone. face: circle A vertex: B The figure has no edges. esolutions Manual - Powered by Cognero Page 5
15. Draw the top view and side view of the drum. Then draw and describe the shape resulting from a vertical cross section of the figure. A vertical cross section of the drum is a rectangle. Find the volume of each prism. 16. The volume of the prism is 60 cubic inches. 17. The volume of the prism is 60 cubic centimeters. esolutions Manual - Powered by Cognero Page 6
18. A shipping box is 11 inches long, 8.5 inches wide, and 5.5 inches high. What is the volume of the box? The volume of the box is 514.25 cubic inches. 19. Sandra is filling a keepsake storage box that is 40.5 centimeters long, 28 centimeters wide, and 17 centimeters high. What is the volume of the box? The volume of the box is 19,278 cubic centimeters. Find the volume of each cylinder. Round to the nearest tenth, if necessary. 20. The volume of the cylinder is about 445.3 cubic centimeters. 21. The radius of the base is half the diameter, so 6 2 = 3. The volume of the cylinder is about 282.7 cubic inches. esolutions Manual - Powered by Cognero Page 7
22. A 12-ounce can of soda measures inches high with a radius of inches. Find the amount of soda that can fit in the can. Round to the nearest tenth. The amount of soda that can fit in the can is about 18.9 cubic inches. Find the volume of each figure. Round to the nearest tenth, if necessary. 23. The volume of the pyramid is 8 cubic inches. 24. The volume of the sphere is about 1436.8 cubic meters. esolutions Manual - Powered by Cognero Page 8
25. Mr. Owens built a conical storage shed with a base 14 feet in diameter and a height of 11 feet. What is the volume of the shed? The radius of the base is half the diameter, so 14 2 = 7. The volume of the shed is about 564.4 cubic feet. Find the lateral and surface area of each prism. Round to the nearest tenth, if necessary. 26. The lateral area of the prism is 68 square centimeters and the surface area is 101 square centimeters. esolutions Manual - Powered by Cognero Page 9
27. The lateral area of the prism is about 143.6 square meters and the surface area is about 166.4 square meters. 28. Sarah is wrapping a gift that is 12 inches long, 6 inches wide, and 4 inches high. How many square inches of paper are needed to cover the gift? To determine the number of square inches of paper needed, find the surface area of the gift. To cover the gift, 288 square inches of wrapping paper are needed. esolutions Manual - Powered by Cognero Page 10
Find the lateral and surface area of each cylinder. Round to the nearest tenth, if necessary. 29. The radius of the base is half the diameter, so 9 2 = 4.5. The lateral area of the cylinder is about 378.9 square feet and the surface area is about 506.1 square feet. 30. The lateral area of the cylinder is about 298.5 square feet and the surface area is about 865.5 square feet. esolutions Manual - Powered by Cognero Page 11
31. 32. The lateral area of the cylinder is about 131.9 square meters and the surface area is about 188.5 square meters. The lateral area of the cylinder is about 202.3 square millimeters and the surface area is about 335.3 square millimeters. esolutions Manual - Powered by Cognero Page 12
33. A cable is covered by rubber sheathing and has a diameter of 3 millimeters. How much rubber sheathing is there in 100 centimeters of cable? To determine the amount of rubber sheathing in 100 centimeters of cable, find the lateral area of the cable. The radius of the cable is half the diameter, so 3 2 = 1.5. Convert the millimeters to centimeters by dividing 1.5 by 10. Since 1.5 10 = 0.15, the radius of the cable is 0.15 centimeters. There is about 94.2 square centimeters of rubber sheathing in 100 centimeters of cable. Find the lateral and surface areas of each figure. Round to the nearest tenth, if necessary. 34. The lateral area of the square pyramid is 244.8 square centimeters and the surface area is 308.8 square centimeters. esolutions Manual - Powered by Cognero Page 13
35. 36. The lateral area of the cone is about 263.9 square feet and the surface area is about 417.8 square feet. The lateral area of the cone is about 131.9 square inches and the surface area is about 182.2 square inches. esolutions Manual - Powered by Cognero Page 14
37. The lateral area of the pyramid is 52.5 square meters and the surface area of the pyramid is 68 square meters. 38. A pyramid-shaped roof has a slant height of 18 feet and its square base is 55 feet wide. How many square feet of roofing material is needed to cover the roof? To determine the amount of roofing material needed to cover the roof, find the lateral area of the roof. So, 1980 square feet of roofing material is needed to cover the roof. esolutions Manual - Powered by Cognero Page 15