11.3 and 11.5: pyramids and cones

11.3 and 11.5: Pyramids and Cones

Pyramids

Pyramid – A 3-D figure with one face (the base) that is any polygon and the other faces (the lateral faces) are triangles that meet at a common vertex.

Regular Pyramid – Base is a regular polygon.

Slant Height (l ) – The length of an altitude of a lateral face of the pyramid.

How are the height and slant height related to the edge of the base of a pyramid???

Surface Area of Pyramids

THEOREM 11.3 – Surface Area of Regular PyramidThe surface area of a regular pyramid is the sum of the lateral area and the area of the base.

BpB 2

1S.A.or L.A.S.A.

Surface Area of Pyramid

The Great Pyramid of Giza, Egypt has a height of 481 ft. Each edge of its square base is about 756 ft. Find the area of the surface of the pyramid.

Cones

Cone – A 3-D figure with a circular base and a curved lateral surface

How are the radius, height, and slant height related???

Surface Area of Cones

THEOREM 11.4 – Surface Area of ConeThe surface area of a cone is the sum of the lateral area and the area of the base.

2S.A.or L.A.S.A. rrB

Find the surface area of the following cone.

Surface Area of Cones

The radius of the base of a cone is 5 m. If the height of the cone is 12 m, find the surface area in terms of π.

Volume of Pyramids

THEOREM 11.8 – Volume of PyramidThe volume of a pyramid is one third the product of the area of a base and the height of the pyramid.

BhV3

1

The Pyramid arena in Memphis, TN has a base of area 300,000 ft2. Its height is 321 ft. What is the volume of the pyramid?

Volume of Pyramids

Find the volume of the following pyramid.

Volume of Cones

THEOREM 11.9 – Volume of ConeThe volume of a cone is one third the product of the area of the base and the height of the cone.

hrVBhV 2

3

1or

3

1

Find the volume of the following cone in terms of π.

Volume of Cones

Find the volume of the following cone in terms of π.

11.3 and 11.5: Pyramids and Cones

Homework:

p.620 #1-13 odd, 18

p.634 #7-14, 18