Common Core Standards: Math
High School: Geometry
Geometric Measurement and Dimension HSG-GMD.A.3
3. Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
Just about everything is in 3D nowadays. We're not saying that math is a trendsetter or anything, but these volume formulas speak for themselves.
Basically, as long as students know these formulas, what they mean, and how to use them, they should be good to go.
Students should also know that oblique solids deserve obliqual—er, equal—treatment. Cavalieri tells us that even though oblique solids are tilted, we can calculate their volumes using these same formulas. Well, he would tell us that if he were still alive.
If students need some hands on activities to really cement these formulas into their brains, you could always bring empty (and clean!) plastic containers from home. Mustard bottles, pickle jars, cake pans, or your favorite coffee mug.
Have them measure these containers and approximate their volumes using the formulas. Then, have them check their results by measuring the volume of water the containers actually hold. (Warning: your classroom may or may not become a splash zone.)
- Surface Area of Cylinders
- Volumes of Pyramids and Cones
- All You Need to Know About Volumes of Prisms and Cylinders