CCSS.Math.Content.8.G.C.9
The standard
Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
Common Core State Standards for Mathematics · Geometry
What this standard means
Students need to know the volume formulas for cylinders, cones, and spheres, then choose the right one for a given problem. They should identify radius, diameter, height, and units from words, diagrams, or objects. They also need to substitute values correctly and state answers in cubic units.
Mastery looks like picking the correct formula without guessing, using diameter to find radius, and explaining why a cone is one-third of a matching cylinder. Students often mix up area and volume, forget to cube units, use diameter as radius, or round too early.
Ways to teach it
- Hands-on activity: Fill a cone with rice three times to show it matches the volume of a cylinder with the same radius and height.
- Prompt: Explain how you would find the volume of a soup can, an ice cream cone, and a basketball, naming the needed measurements.
- Quick assessment: Give three diagrams with extra measurements and ask students to choose the formula, substitute values, and include cubic units.
- Real-world connection: Have students compare two drink container sizes using volume formulas to decide which package holds more.
Plan a lesson for CCSS.Math.Content.8.G.C.9
Generate a complete lesson plan aligned to this standard, with objectives, activities, and materials. Free, no account needed.
Related standards
- CCSS.Math.Content.8.G.C
Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
- CCSS.Math.Content.HSG-GMD.A.3
Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
- CCSS.Math.Content.7.G.B
Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
- CCSS.Math.Content.6.G.A
Solve real-world and mathematical problems involving area, surface area, and volume.