Name:______________________________________________________ Date: _______________ Geometry 2013-2014 Solid Geometry Name:______________________________ Teacher:____________________________ Pd: _______ Table of Contents DAY 1: SWBAT: Calculate the Volume of Prisms and Cylinders Pgs: 1 - 7 HW: Pgs: 8 - 10 DAY 2: SWBAT: Calculate the Volume of Pyramids and Cones Pgs: 11 - 15 HW: Pgs: 16 - 17 DAY 3: SWBAT: Calculate the Surface Area of Rectangular Prisms and Cylinders Pgs: 18 - 23 HW: Pgs: 24 - 25 DAY 4: SWBAT: Calculate the Surface Area of “Other” Prisms Pgs: 26 - 30 HW: Pgs: 31- 32 DAY 5: SWBAT: Calculate the Surface Area of Pyramids and Cones Pgs: 33 - 37 HW: Pgs: 38- 39 DAY 6: SWBAT: Calculate the Volume and Surface Area of Spheres Pgs: 40 - 43 HW: Pgs: 44 - 45 Day 7: SWBAT: Calculate the Volume and Surface Area of Three Dimensional Figures (REVIEW) Pgs: 46 - 47 Day 8: SWBAT: Calculate the Volume and Surface Area of Three Dimensional Figures (REVIEW) Pgs: 48 - 51 Summary Page Pg: 52 Extra Credit Pg: 53 Basic Area Formulas s VOLUME LATERAL AREA SURFACE AREA SWBAT: Calculate the volume of prisms and cylinders Volume of rectangular solids and cylinders – Day 1 Warm – Up: Read this section and Complete the puzzle on page 2. Three-dimensional figures, or solids, can be made up of flat or curved surfaces. Each flat surface is called a face. An edge is the segment that is the intersection of two faces. A vertex is the point that is the intersection of three or more faces. Each face of a solid figure is called either a base or a lateral face. Solid figures generally have one or two bases. If it has two, these bases are parallel. If a figure has two parallel bases and lateral faces, such as in a prism, the bases will be perpendicular to the lateral faces. A polyhedron is formed by four or more polygons that intersect only at their edges. Prisms and pyramids are polyhedrons, but cylinders and cones are not. 1 Co 2 Shape Name Formula Example 2. 25 ft 3. 4. 5. 3 Shape Name Formula Example 6. 7. 8. 9. 4 Calculate the volume of each cylinder. Write your answers in terms of and to the nearest tenth. 10. 11. Working Backwards 12. 13. A cube has a volume of 3375 cubic units. Calculate the length of one side of the cube. 5 14. The volume of a cylinder is 441 in3. The height of the cylinder is 9 in. Calculate the radius of the cylinder to the nearest tenth of a centimeter. 15. The volume of a cylinder is 794.3 cm3. The height of the cylinder is 7 cm. Calculate the radius of the cylinder to the nearest tenth of a centimeter. Challenge 6 Summary: Exit Ticket: 7 Homework - Volume of Prisms and cylinders – Day 1 Calculate the volume of each. 1. 2. 3. 4. 5. 6. Round your answers to the nearest tenth. 8 7. Round your answers to the nearest hundredth. 8. Leave your answer in terms of . Word Problems 9. The volume of a cube is 216 cubic yards. Find the side length. 10. Julia has a rectangular prism with a length of 10 centimeters, a width of 2 centimeters, and an unknown height. He needs to build another rectangular prism with a length of 5 centimeters and the same height as the original prism. The volume of the two prisms will be the same. Find the width, in centimeters, of the new prism. 11. 12. 9 13. 14. A right circular cylinder has a volume of 2,000 cubic inches and a height of 4 inches. What is the radius of the cylinder to the nearest tenth of an inch? 15. 10 SWBAT: Calculate the Volume of Pyramids and Cones Warm - Up Calculate the volume of the prism below. a) If the dimensions are doubled. b) If the dimensions are divided by 5. Volume of a Pyramids and Cones 11 l Shape Name Formula Example 1. 2. 3. 12 4. 5. 6. 7. 8. 13 Word - Problems 9. The Volume of a square pyramid is 507 meter cubed. If the height is 9 meters, then find the dimensions of the base? 10. A cube with sides 5 inches, and a pyramid with base edges 5 inches. What is the height, so that the volume of the cube and the pyramid are equal? 11. A right cone has a height of 6 feet and a volume of 32 cubic feet. What is its radius? 12. Sand is piled in the shape of a cone. If a pile of sand has a diameter of 20 feet and a volume of 610 feet cubed, then what is the height of the pile? 14 Challenge Calculate the volume of the composite figure. Summary Calculate the volume of each shape. a. b. Exit Ticket 15 Homework - Volume of Pyramids and Cones – Day 2 Calculate the volume of each. 1. 2. 3. ***4. 5. 6. 7. 8. 16 Word Problems 9. The volume of a square pyramid is 605 . Calculate the dimensions of the base of the square if the pyramid has a height of 15m. 10. The Volume of square pyramid is 784 . If the base edge is 14 centimeters, then how tall is the pyramid? 11. A cone has a volume of 432 and a height of 9 cm. a) Calculate the radius of the cone b) Calculate the slant height of the cone. 12. If the volume of a cone is 10 what is its height if the area of the base is 10 m2 ? 17 Surface area of rectangular prisms and cylinders – Day 3 Warm – Up Rectangular Prism SA=2lh + 2hw + 2lw This formula assumes a "closed box", with all 6 sides 18 Example 1: Calculate the surface area of the prism below. Example 2: Rashid needs to buy some wood to build a box. He must calculate the surface area of the box to determine how much wood to buy. A diagram of the box is shown below. How much wood does Rashid need to buy to build the box? Example 3: The surface area of the prism below is 102 cm2. Find x 19 Example 4: Calculate the surface area of a cube with a side that measures 5 in. Example 5: The surface area of a cube is 24 cm2. Find the length of each side of the cube. 20 Surface Area of a Cylinder = Example 6: Find the surface area, to the nearest tenth of a square foot. 21 7. Calculate the surface area, to the nearest tenth of a square foot. 8. A cylinder has a surface area of 200 ft2. a) Calculate the radius of the cylinder if the height is 15 feet. b) Calculate the Lateral Area of the cylinder. 9. 22 Challenge Problem: What is the surface area of the composite figure below? Summary: Exit Ticket 23 Homework - Surface area of rectangular prisms and cylinders – Day 3 1. Find the surface area, to the nearest tenth of a square foot, of this container assuming it has a closed top and bottom. 2. Find the surface area of the prism below. 11cm 3cm 6 cm 3. Find the surface area of the cylinder below. 4. Calculate the surface area of a cube with a side of 6 inches. 24 5. Solve for x given the surface area. 6. A cube has a surface area of 486 cm2. Calculate the length of one side of the cube. 7. The surface area of a cylinder is 48 square feet. The radius of the cylinder is 3 feet. What is the height of the cylinder? 8. Solve for z given the surface area. 25 Surface area of “Other” prisms – Day 4 Warm – Up Calculate the surface area of the cube below. 10 inches Describe the effect of each change on the surface of the given figure. a) If the dimensions are doubled. b) If the dimensions are divided by 5. 26 Shape Procedure for Calculating Surface Area 1. Name _______________________ 2. Name _______________________ 3. Name _______________________ 27 4. Name _______________________ 5. Name _______________________ 6. Name _______________________ 28 Word Problems 7. 8. 9. 29 Challenge A builder drills a hole through a cube of concrete, as shown in the figure. This cube will be an outlet for a water tap on the side of a house. Find the surface area of the figure. Exit Ticket Calculate the surface area of the triangular prism to the nearest hundredth. 30 Homework – Day 4 Calculate the Lateral and Surface area of each. Show your work here! 1. 2. 3. 4. 31 Word Problems 5. The lateral area for a hexagonal prism measures 432 inches2. Calculate the surface area of the prism if the height of the prism measures 9 inches. 6. The lateral area for a regular triangular prism measures 462 inches2. Calculate the surface area of the prism if the height of the prism measures 11 inches. 7. The surface area for a right triangular prism measures 864 cm2. The legs of the triangle measure 12 and 16 cm respectively. Calculate the height and Lateral Area of the prism. (Draw a picture to help you!) 32 Surface Area of Pyramids and Cones – Day 5 Warm – Up 1. 2. Pyramids l 33 Example 1: Find the L.A. and S.A. Example 2: Example 3: **Challenge*** 34 Example 4: Cones 35 Example 5: Calculate the lateral area and surface area. Example 6: Calculate the lateral area and surface area. Word Problems 7. Find the surface area of a regular square pyramid with slant height 7 in, if its lateral area is 70 sq.