Grade 8 Lesson plan
Fernhaugh Digester: Why a Cone Holds One Third of a Cylinder
A grade 8 lesson where students compare a cone and a cylinder of equal size, then find the volume of a fictional digester with a cone bottom.
Common Core Math · Grade 8
8.G.C.9 Find volumes of cones, cylinders, and spheres
Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
Why water teaches this standard well
Students apply the cylinder volume formula to size a water tower's cylindrical tank, finding how many gallons it holds from its height and diameter. This is the exact formula, and the exact kind of structure, that appears on real operator-certification exams.
Materials tagged with this code are written to the full standard , and each carries a written note explaining the alignment. See how we review materials.
21 materials aligned to 8.G.C.9
Lesson plans
Grade 8 Lesson plan
Coldspar Reservoir Sediment: Storage Loss and Delta Volume
A grade 8 science lesson tracing rock from a fictional watershed into reservoir sediment, with survey math on storage loss and a cone-volume estimate of the delta.
Worksheets
Grade 8 Worksheet
Quarrymoor Reuse Tanks: Finding a Missing Dimension From Volume
A grade 8 worksheet on a fictional reclaimed water site where students find cylinder, cone, and sphere volumes and then work backward to a missing depth or radius.
Grade 8 Worksheet
Confluence Plaza Fountain: A Water-Sculpture Volume Worksheet
A grade 8 art-design worksheet where students size a public fountain's cylinder, cone, and sphere forms with volume formulas and a cubic-foot-to-gallon conversion.
Grade 8 Worksheet
Dunmarsh Booster Station: Volume of a Cylindrical and Spherical Tank
A grade 8 worksheet where students find the volume of a fictional pump station's cylindrical storage tank and spherical pressure tank in cubic feet and gallons.
Math problem sets
Grade 8 Math problem set
Quarry Bend's Elevated Tank: Stored Energy and Water Pressure
A grade 8 science problem set where students find the weight and stored potential energy of water in a fictional elevated tank and explain why height sets pressure.
Grade 8 Math problem set
Otterbourne's Digester Tanks: Volume Math for a Biosolids Operator
A grade 8 problem set where students use cylinder, cone, and sphere volume formulas to check the capacity of a fictional digester, grit hopper, and biogas holder.
Grade 8 Math problem set
Sablerock's Pressure Filters: A Cylinder Volume and Loading-Rate Set
A grade 8 engineering set that sizes cylindrical pressure filters, converts volume to gallons, and checks loading rates against a safe design range.
Grade 8 Math problem set
Blackstock Treatment Plant Tanks: Cylinder, Cone, Sphere Volume
A grade 8 problem set on the volume formulas for a cylinder, a cone, and a sphere, applied to three tanks at a fictional drinking-water treatment plant, with fill time.
Grade 8 Math problem set
Netherby Sludge Thickener: Cone, Cylinder, and Sphere Volumes
A grade 8 problem set finding the volume of a fictional plant's cone-bottomed tank and a spherical digester, converting cubic feet to gallons and comparing sizes.
Grade 8 Math problem set
Vellacott Dam Penstock, Trap, and Air Chamber: Cylinder, Cone, Sphere
A grade 8 problem set finding the volume of a pipe, a cone-shaped sediment trap, and a spherical air chamber at a fictional hydropower dam.
Grade 8 Math problem set
Sizing Corvale's Stormwater Detention Basin: A Cylinder Volume Set
A grade 8 problem set using the rational runoff method and cylinder volume formula to size an underground detention basin for a fictional paved business park.
Grade 8 Math problem set
Bramblewood Middle School Cistern: Cylinder Volume and Roof Runoff
Nine problems sizing a fictional school's cylindrical stormwater cistern against roof runoff, using the real cylinder-volume and roof-runoff formulas.
Classroom activities
Grade 8 Classroom activity
Rain Barrel Design Studio: Sizing and Decorating a Storm-Ready Cistern
A grade 8 design-studio activity where students size a cylindrical rain barrel using the real volume formula, then create and score original artwork for its exterior.
Projects
Grade 8 Project
Brindlecombe Constructed Wetland: A Grade 8 Sizing Project
A four-session grade 8 project where teams build a flow function, size a treatment wetland and a holding tank, and pitch the design to a fictional village board.
Grade 8 Project
Sizing a Water Tower for Cottonwood Estates: A Volume and Cost Project
A four-session grade 8 project where teams size a cylindrical water tower, then use a system of equations to choose the cheaper of two suppliers within a fixed budget.
Quizzes & test questions
Grade 8 Quiz & test questions
Oldcastle Mill Race Micro-Hydro: A Design Screening Quiz
A 20-point grade 8 quiz on screening a micro-hydro project, mixing constraint identification with forebay volume, pressure, and flow conversion computations.
Grade 8 Quiz & test questions
Kingfisher Mills Water System: A Grade 8 Volume and Functions Test
A grade 8 unit test on a fictional town's water system covering scientific notation, tank volume, systems of equations, and linear functions.
Grade 8 Quiz & test questions
Ospreyville Phosphorus Cleanup: A Grade 8 Unit Test
A grade 8 unit test on functions, unit rates, linear equations, and volume, set in a fictional town reducing phosphorus in the Sallowbrook River.
Grade 8 Quiz & test questions
Redhawk Water System Benchmark: Systems, Volume, and Data
A grade 8 unit test covering scientific notation, cylinder volume, systems of equations, and scatter plots, with multiple-choice and computation items.
Grade 8 Quiz & test questions
Amberlake's New Elevated Tank: A Grade 8 Volume and Cost Assessment
A grade 8 assessment on a fictional water authority's elevated tank, testing cylinder volume, scientific notation, and a systems-of-equations cost comparison.