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More about Volumes and Surface Areas
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1. Cavalieri's Principle
- Cavalieri's Principle (祖暅原理)
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2. Volume of Pyramids
- Trisecting the Cube into 3 Pyramids
- Volume of Pyramids
- Volume of Pyramids - Chinese Proof
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3. Curved Surface Area of Cones
- Curved Surface Area of Cones (Combined Version)
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4. Volume and Surface Area of Spheres
- Volume of Spheres
- Surface Area of Spheres
- Volume of Spheres with Proof
- Surface Area of Spheres with Proof
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5. Relationships between Volumes and Surface Areas of Similar Figures
- Volumes and Surface Areas of Similar Cuboids
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More about Volumes and Surface Areas
GeoGebra Institute of Hong Kong, Dec 3, 2014
GeoGebraBook for explaining the formulas for volumes and surface areas of pyramids, circular cones and spheres.
Table of Contents
- Cavalieri's Principle
- Cavalieri's Principle (祖暅原理)
- Volume of Pyramids
- Trisecting the Cube into 3 Pyramids
- Volume of Pyramids
- Volume of Pyramids - Chinese Proof
- Curved Surface Area of Cones
- Curved Surface Area of Cones (Combined Version)
- Volume and Surface Area of Spheres
- Volume of Spheres
- Surface Area of Spheres
- Volume of Spheres with Proof
- Surface Area of Spheres with Proof
- Relationships between Volumes and Surface Areas of Similar Figures
- Volumes and Surface Areas of Similar Cuboids
Cavalieri's Principle (祖暅原理)
Acknowledgement: Inspired by Steve Phelps' applet "Figure 6.7 Cavalieri's principle".
Trisecting the Cube into 3 Pyramids
Anthony Or. GeoGebra Institute of Hong Kong.
Curved Surface Area of Cones (Combined Version)
Volume of Spheres
The figure shows a hemisphere of radius r and a cylinder of base radius and height r with an inverted cone of the same height and base radius removed. Drag the red point to see the cross-sections of the two solids at a height h.
(a) Express x and y in terms of r and h.
(b) Are the cross-sections equal in area?
(c) Hence show that the volume of the sphere of radius r is 4/3 π r³.
Volumes and Surface Areas of Similar Cuboids
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