CCSS.Math.Content.HSG-GMD.A.3
The standard
Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
Common Core State Standards for Mathematics
What this standard means
Students need to choose the right volume formula for a cylinder, pyramid, cone, or sphere, plug in measurements correctly, and solve for volume or a missing dimension. They should track units, use radius instead of diameter, and handle exact answers with pi or decimal approximations when asked.
Mastery looks like reading a problem, sketching the solid, labeling known values, selecting the formula, and explaining each step. Common trouble spots are mixing up area and volume, forgetting the one-third factor for cones and pyramids, using diameter as radius, and rounding too early.
Ways to teach it
- Hands-on activity: Give groups cans, paper cones, boxes, and balls, then have them measure dimensions and calculate each object's volume.
- Writing prompt: Explain why a cone with the same base and height as a cylinder has one-third the volume.
- Quick assessment: Show four solids with labeled dimensions and ask students to write only the correct formula setup for each.
- Real-world connection: Have students compare two drink containers and decide which holds more, using measurements from the labels or rulers.
Plan a lesson for CCSS.Math.Content.HSG-GMD.A.3
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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.1
Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone.
- CCSS.Math.Content.8.G.C.9
Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
- CCSS.Math.Content.HSG-GMD.A
Explain volume formulas and use them to solve problems