Stack a Circular Base through a Height
A cylinder with a constant circular cross-section has volume equal to base area times perpendicular height.
About 20 minutes, plus any extended practice
Open lesson 1Geometry: Curved Solids and Volume Scaling
Three-dimensional formulas relate solid shapes to base areas, heights and radii. Similar solids change every corresponding length together, making volume respond to the cube of a scale factor rather than its first power.
Before you begin
- Compute circle area; evaluate squares and cubes; use fractions in formulas.
Choose by skill rather than age alone. Read with an adult when useful, revisit a lesson, or explore another grade.
Follow the lesson sequence
Compare a Cone with Its Matching Cylinder
A cone’s volume is one third of a cylinder with the same base area and perpendicular height.
About 20 minutes, plus any extended practice
Open lesson 2Use a Cubed Radius for Sphere Volume
Sphere volume is (4/3)πr³.
About 20 minutes, plus any extended practice
Open lesson 3Cube a Common Length Scale Factor
If all corresponding lengths change by a factor k, base areas change by k² and heights by k.
About 20 minutes, plus any extended practice
Open lesson 4Review and transfer
After the lessons, try 4 new review cases and a practical task. Each answer has an explanation and a link back to the related lesson.
Open the unit reviewGuest answers are temporary. Keep your own paper or document; this unit does not certify completion or record a school grade.
Topic references
- California CCSS mathematics topic reference: topic reference — Geometry: Curved Solids and Volume Scaling
These references informed the topic selection. They do not certify complete standards alignment.