Standard(s):
[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] PRE-19 (9-12) 31 : 31. Graph conic sections from second-degree equations, extending from circles and parabolas to ellipses and hyperbolas, using technology to discover patterns.
a. Graph conic sections given their standard form.
Example: The graph of x2/9 + (y-3)2/4=1 will be an ellipse centered at (0,3) with major axis 3 and minor axis 2, while the graph of x2/9 + (y-3)2/4=1 will be a hyperbola centered at (0,3) with asymptotes with slope ±3/2.
b. Identify the conic section that will be formed, given its equation in general form.
Example: 5y2 - 25x2=-25 will be a hyperbola.