Volumes of Pyramids and Cones

1
Section 10.6

• Volumes of Pyramids and Cones

2
Theorem 10-8Volume of a pyramid

• The volume of pyramid is one third the product of
  the area of the base and the height of the pyramid

V 1/3 Bh
3
Arena in Memphis, Tennessee

• The arena is in the shape of a pyramid.
• The area of the base of the arena is 300,000 ft2
• The height of the arena is 321 ft.
• What is the volume of the arena?

V 1/3 Bh
V 1/3 (300,000 ft2)(321 ft)
V 32,100,000 ft3
4
Theorem 10-9Volume of a Cone

• The volume of a cone is one third the product of
  the area of the base and the height of the cone

V 1/3 Bh or V 1/3 ?r²h
h
B
5
Volume of an Oblique Cone

• V 1/3 ?r²h

V 1/3 (?)(15)²(25)
V 1875? ft3 5890.4862 ft3
25ft
?
30 ft
6
Find the unknown variable

• V 1/3 ?r²h

24? 1/3 (?)(r)²(4)4/3? 4/3?
18 r2
3 v 2 r
4
r
7
Homework

• Page 554
• Problems 2-10e, 11,12,13,14,16-28e