Definition and Formula of Pyramids

1. A pyramid is a solid with a polygon-shaped base and the remaining triangular faces (lateral faces) meeting at a vertex. A pyramid is named according to the shape of its base.
2. In a right pyramid, the vertex is directly above the centre of the base. Otherwise, it is called an oblique pyramid. 
(In this chapter, we will only be studying right pyramids) 
3. In a pyramid, 
(a) the perpendicular height or height is the perpendicular distance from the vertex to the base of the pyramid. 
(b) the slant height is the height of each of the triangular faces. 
(c) the slant edge is the edge where the triangular faces meet each other. 

Definition and Formula of Cones

1. A cone is a solid that has a circular base and a vertex. In other words, it is a pyramid with a circular base. 
2. In a right circular cone, the vertex is directly above the centre of the circular base. Otherwise, it is called an oblique circular cone. 
(In this chapter, we will study only right-circular cones. The term cone will be used to mean a right-circular cone)
3. In a cone,
(a) the perpendicular height or height os the perpendicular distance from the vertex to the base of the cone.
(b) the slant height is the distance from the vertex to the circumference of the cone.
(c) the radius of the cone is the radius of the base. 

Definition and Formula of Spheres

1. A sphere is a solid in which all points on the surface are the same distance from the centre. This distance is the radius of the sphere. 
2. A hemisphere is half of a sphere with a circular base. 

Video Example

Here is a video solving questions involving what you have learnt so far: