Lesson 72, day 2

Pyramids and Cones

Pyramids

• Pyramid: geometric solid with a polygon base, and triangle faces (lateral faces)

• Vertex: top of the pyramid

• Lateral edges: where the lateral faces connect

• Axis: segment from the vertex to the center of the base

• Altitude: perpendicular segment from the vertex to the plane of the base

Pyramids

• Regular pyramids: base is a regular polygon and lateral faces are isosceles triangles

• Slant height: height of a lateral face– Only in regular pyramids

Cones

• Pyramid with a circle for a base

• Lateral surface: curved surface between the vertex and the base

• Axis: like the pyramid

• Altitude: like the pyramid

• Height of a cone and pyramid: length of the altitude

Volume of Pyramids and Cones

BhV3

1

Example 72.4

• Find the volume of the right rectangular pyramid. The height is 8 in.

7 in9 in

Example 72.5

• A right circular cone has a base of radius 6 ft and a height of 8 ft. Find the volume of the cone.

Example 72.6

• Find the surface area of this regular square pyramid. Dimensions are in centimeters.

6 in

5 in

Surface Area of Cones

• Lateral surface area = π·r·l

radius

Slant height

Example 72.7

• A right circular cone has a base of radius 8 m and a slant height of 10 m. Find the surface area of the right circular cone.

Homework

• P.S. 72

• 1-18 all, 21-26 all, 30