Lesson Plan

Decompose a composite 3D figure into standard shapes (prisms, cylinders, cones, hemispheres, pyramids)

Compute the volume of a composite figure by summing component volumes (additive) or subtracting removed volumes (subtractive)

Compute the surface area of a composite figure, correctly removing the contact area where shapes join

Distinguish between additive composites (shapes joined together) and subtractive composites (shapes carved out)

Solve ACT-style composite figure problems efficiently, selecting the right decomposition and applying memorized formulas

G 702. Compute the area of composite geometric figures when planning and/or visualization is required G 601. Use relationships involving area, perimeter, and volume of geometric figures to compute another measure (e.g., surface area for a cube of a given volume and simple geometric probability) G 705. Solve multistep geometry problems that involve integrating concepts, planning, and/or visualization