Unit 11: Circumference, Area, and Volume

California State Standard Geometric Measurement and Dimension G-GMD:
Explain volume formulas and use them to solve problems.
1. Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone.
3.  Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. 
Visualize relationships between two-dimensional and three-dimensional objects.
4. Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.
5. Know that the effect of a scale factor k greater than zero on length, area, and volume is to multiply each by k, k2, and k3, respectively; determine length, area and volume measures using scale factors. CA
California State Standard Modeling with Geometry G-MG
Apply geometric concepts in modeling situations.
1. Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder). 
2. Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).
3. Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).