GCSE Higher Ch7 Area and Volume
Table of Contents
- Circles
- Area of a circle
- Sectors
- Arc Length and Area of a Sector
- Cones
- Net of a Cone
- Curved Surface Area of Cones
- Curved Surface Area of Cones (Combined Version)
- Pyramids
- tisect a cube
- Trisecting the Cube into 3 Pyramids
- Spheres
- Volume of Spheres
- Volume of Spheres with Proof
- Surface Area of Spheres
- Surface Area of Spheres with Proof
- Scale factors
- Volumes and Surface Areas of Similar Cuboids
Area of a circle
Demonstration.
Arc Length and Area of a Sector
Net of a Cone
tisect a cube
This is another way of cutting a cube into congruent pyramids. This shows each pyramid is 1/3 of a cube.
Volume of Spheres
The figure shows a hemisphere of radius [i]r[/i] and a cylinder of base radius and height [i]r[/i] 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 [i]h[/i].[br](a) Express [i]x[/i] and [i]y[/i] in terms of [i]r[/i] and [i]h[/i].[br](b) Are the cross-sections equal in area?[br](c) Hence show that the volume of the sphere of radius [i]r[/i] is 4/3 π [i]r[/i]³.