Integrals and Volumes of Revolution
by Anonymous
Rotate curves and stack cross-sections to compute volume by definite integration, and confirm the 3:2:1 ratio of cylinder, hemisphere, and cone.
About this app
Integrals and Volumes of Revolution is an interactive calculus learning app about finding volume with definite integrals. Explore how rotating curves creates solids with circular cross-sections, stack square, triangular, and semicircular cross-sections, and compare the calculated volumes of cylinders, hemispheres, and cones in the ratio 3:2:1.
Use cases
- High school students learning applications of definite integrals
- Teachers demonstrating solids of revolution and cross-sectional volume
- Learners reviewing volume formulas through visual interaction
- Students practicing how changing a curve or endpoint affects volume
Features
- Rotate selectable curves to visualize cylinders, cones, and other solids
- Adjust the right endpoint and view the resulting volume calculation
- Build volumes by stacking square, equilateral-triangle, or semicircular cross-sections
- Compare cylinder, hemisphere, and cone volumes with interactive vessel selection
- Guided missions with reset and next-step controls