[MA2015] GEO (9-12) 35 :
35 ) Give an informal argument for the formulas for the circumference of a circle; area of a circle; and volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri's principle, and informal limit arguments. [G-GMD1]
[MA2015] PRE (9-12) 38 :
38 ) (+) Give an informal argument using Cavalieri's principle for the formulas for the volume of a sphere and other solid figures. [G-GMD2]
[MA2019] REG-7 (7) 19 :
19. Describe the two-dimensional figures created by slicing three-dimensional figures into plane sections. [MA2019] REG-8 (8) 30 :
30. Use formulas to calculate the volumes of three-dimensional figures (cylinders, cones, and spheres) to solve real-world problems. [MA2019] GEO-19 (9-12) 16 :
16. Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects. [MA2019] GEO-19 (9-12) 17 :
17. Model and solve problems using surface area and volume of solids, including composite solids and solids with portions removed.
a. Give an informal argument for the formulas for the surface area and volume of a sphere, cylinder, pyramid, and cone using dissection arguments, Cavalieri's Principle, and informal limit arguments.
b. Apply geometric concepts to find missing dimensions to solve surface area or volume problems. [MA2019] GEO-19 (9-12) 23 :
23. Develop definitions of rotation, reflection, and translation in terms of angles, circles, perpendicular lines, parallel lines, and line segments.