Volume of Prisms and Cylinders
One formula rules all prisms and cylinders: Volume = base area × height. For a cylinder, the base is a circle, so V = πr²h. Students who understand why this works — it's the same logic as layering — can derive the formula from first principles rather than memorizing it.
What students explore
One formula rules all prisms and cylinders: Volume = base area × height. For a cylinder, the base is a circle, so V = πr²h. Students who understand why this works — it's the same logic as layering — can derive the formula from first principles rather than memorizing it.
Key ideas
Calculate the volume of prisms using V = base area × height. Calculate the volume of cylinders using V = π × r² × h. Solve problems involving volume in real-world contexts. Compare volumes of different shapes and containers.
Putting it together
Apply these ideas through hands-on activities, guided practice, and real-world problems.