Curriculum placement
Geometry. This describes the skill, not a learner estimate.
Volumes of cylinders, cones, pyramids, spheres
Solve contextual cylinder pyramid cone and sphere volume problems
Problem types
- Volume, density and unit chains
- Volumes of solids in context
- Weight, mass or trips from a solid's volume
- Show the work: weight, mass or count from a solid's volume and a density
Builds on
- Volume of cylinders, cones, and spheres
- Surface area of prisms and pyramids
- Cavalieri's principle · Useful idea
Equal cross-sections show that an oblique solid has the volume of the right solid with the same base and perpendicular height.
- How a dilation changes a figure · Useful idea
A scale factor k multiplies lengths by k and volumes by k cubed, which models scaled solids.
- Cross-sections and solids of revolution · Useful idea
A rotated rectangle, right triangle or semicircle sweeps out a cylinder, cone or sphere, whose volume formula gives the volume.
- Area and volume of composite figures · Useful idea
The volume of a composite solid adds the volumes of simpler solids and is used to model real objects.
- Volume with fractional edge lengths · Useful idea
Volumes of prisms with fractional edges are used to find volumes of composite solids in a modeling situation.
Leads to
- Modeling density · See it applied
Mass is density times volume, so a solid's volume formula gives the mass of a rod or block of known density.
- Designs that meet geometric constraints · See it applied
A design with a required volume leads to a constraint on its dimensions, such as the volume of a container.
- Quadratic, rational, and exponential constraints · See it applied
A volume formula in one unknown dimension gives a polynomial equation, often quadratic after a ratio of dimensions is fixed.
Related skills
- Modeling with geometry · Shared foundations
Open the interactive map to explore lessons and skill connections.