Surface Area and Volume of Solids
How much skin a solid has and how much space it fills. Surface area is every outward face added once, so faces that touch stop counting; volume is a base stacked to a height, so cutting a piece away removes exactly that piece. Both run backwards too: a known area or volume gives back a missing edge.
grade 6–8 GeometryMeasurement & data Visualize Spatial RelationshipsIdentify Subproblems
Progression (13)
g6 1. Build the prism from its top, front and side views Geometry
g6 2. Same boxes, different stacking, different surface area Geometry
g7 3. Surface area is the sum of every face Geometry
g6 4. Volume needs every length in the same unit GeometryMeasurement & dataRatios
g6 5. Count how many fit along each edge GeometryMeasurement & data
g7 6. Cutting a piece away removes that much volume Geometry
g6 7. Work back from volume or surface area to a missing edge GeometryExpressions
g6 8. A submerged stone displaces its own volume Geometry
g7 9. Scaling every edge by ■ scales volume by ■ cubed Geometry
g7 10. Volume is the base stacked to the height Geometry
g8 11. Same height, radius times ●, volume times ● squared Geometry
g7 12. Get a cylinder's height or radius back from its surface area GeometryExpressions
g7 13. Surface area is the sum of every face Geometry