Geometry: Notes
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1 Geometry: Notes NAME 11.5 Volumes of Prisms and Cylinders Date: Define Vocabulary: volume Cavalieri s Principle density similar solids Examples: Finding Volumes of Prisms 1
2 Examples: Finding Volumes of Prisms Examples: Finding Volumes of Cylinders 2
3 Examples: Using the Formula for Density The density of water is 1000 kilograms per cubic meter. Find the mass of 1 cubic foot of water. Use the fact that 1 foot = meters. The diagram shows the dimensions of a concrete cylinder. Concrete has a density of 2.3 grams per cubic centimeter. Find the mass of the concrete cylinder to the nearest gram. Assignment 3
4 11.5 Volumes of Prisms and Cylinders Date: Examples: Modeling with Mathematics You are building a cylindrical packing tube. You want the length of the tube to be 30 inches and the volume to be 589 cubic inches. What should the radius of the base be? You are building a rectangular chest. You want the length to be 5 meters, the width to be 3 meters, and the volume to be 60 cubic meters. What should the height be? Examples: Solving a Real-Life Problem You are building a 3-foot tall dresser. You want the volume to be 42 cubic feet. What should the area of the base be? Give a possible length and width. You are building a 5-meter-tall dresser. You want the volume to be 75 cubic meters. What should the area of the base be? Give a possible length and width. 4
5 Examples: Finding the Volume of a Similar Solid Square prism A and square prism B are similar. Each base edge of prism A is 4 inches, and each base edge of prism B is 6 inches. The volume of prism B is 135 cubic inches. Find the volume of prism A. Examples: Finding the Volume of a Composite Solid Find the volume of the composite solid. Assignment 5
6 11.6 Volumes of Pyramids Date: Define Vocabulary: pyramid composite solid Examples: Finding the Volume of a Pyramid 6
7 Examples: Using the Volume of a Pyramid A square pyramid has a height of 12 centimeters and a volume of 64 cubic centimeters. Find the side length of the square base. The volume of a square pyramid is 75 cubic meters and the height is 9 meters. Find the side length of the square base. Examples: Using the Volume of a Pyramid Find the height of the triangular pyramid. 7
8 Examples: Finding the Volume of a Similar Solid Square pyramid A and square pyramid B are similar. The height of pyramid A is 6 inches and the height of pyramid B is 15 inches. The volume of pyramid B is cubic inches. Find the volume of pyramid A. Pyramid C and pyramid D are similar. Find the volume of pyramid D. Examples: Finding the Volume of a Composite Solid Assignment 8
9 11.7 Surface Areas and Volumes of Cones Date: Define Vocabulary: lateral surface of a cone Examples: Finding Surface Areas of Right Cones Find the surface area of the right cone. 9
10 Examples: Finding the Volume of a Cone Find the volume of the cone
11 Examples: Finding the Volume of a Similar Solid Cone A and cone B are similar. The height of cone A is 6 inches and the height of cone B is 2 inches. The volume of cone B is 18π cubic inches. Find the volume of cone A. Cone C and cone D are similar. Find the volume of cone D. Examples: Finding the Volume of a Composite Solid Assignment 11
12 11.8 Surface Areas and Volumes of Spheres Date: Define Vocabulary: chord of a sphere great circle Examples: Finding the Surface Areas of Spheres 12
13 Examples: Finding the Diameter of a Sphere Examples: Finding the Volume of a Sphere 1. The radius of a sphere is 5 yards. Find the volume of the sphere. 2. The diameter of a sphere is 36 inches. Find the volume of the sphere. 13
14 Examples: Finding the Volume of a Sphere The surface area of a sphere is 676π square inches. Find the volume of the sphere. The surface area of a sphere is 576π square centimeters. Find the volume of the sphere. Examples: Finding the Volume of a Composite Solid Find the volume of the composite solid. Assignment 14
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