Unit 7 - Equations and measurement
- Students should be able to verify experimentally the formulas for the volume of a cylinder, pyramid, sphere, prism and cone; emphasize volume as the product of the area of the base and the height for both prisms and cylinders.
- Students should be able to use and explain Cavalieri’s Principle to show that the volume of an oblique solid can be found using right solids.
- Students should find the volume of solids and composite solids to explain real-life phenomena.
- Prism – a solid figure that has the same cross section all along its length
- Students should be able to choose the appropriate geometric solid to approximate volumes of irregular objects.
- Students should be able to choose the appropriate geometric figure or solid to approximate density of irregular objects in a geometric situation.
Textbook Connections
Module 2-5 Three Dimensional Figures
Students find measures of three-dimensional figures.
Module 11-6 Volumes of Prisms and Pyramids
Students find volumes of prisms and pyramids by using the formulas they derive.
Module 11-7 Volumes of Cylinders, Cones, and Spheres
Students find volumes of cylinders, cones, and spheres by using the formulas they derive.
Module 11-8 Applying Similarity to Solid Figures
Students find measures of similar figures and solids by using scale factors.
Module 11-9 Density
Students solve real-world problems involving density by using area and volume.
Module 2-5 Three Dimensional Figures
Students find measures of three-dimensional figures.
Module 11-6 Volumes of Prisms and Pyramids
Students find volumes of prisms and pyramids by using the formulas they derive.
Module 11-7 Volumes of Cylinders, Cones, and Spheres
Students find volumes of cylinders, cones, and spheres by using the formulas they derive.
Module 11-8 Applying Similarity to Solid Figures
Students find measures of similar figures and solids by using scale factors.
Module 11-9 Density
Students solve real-world problems involving density by using area and volume.