Volume of Pyramids and Cones

1
11-6

• Volume of Pyramids and Cones
• Pages 615-620
• May 9th 2006

2
Vocabulary

• Volume of a Right Circular Cone- If a right
  circular cone has a volume of V cubic units, a
  height of h units, and the area of the base is B
  square units, then V1/3Bh.
• Volume of a right pyramid- If a right pyramid has
  a volume of V cubic units, a height of h units,
  and the area of the base is B square units, then
  V1/3Bh.
• Cavalieris Principle- If two solids have the
  same height and the same cross-sectional area at
  every level, then they have the same volume.

3
Example 1!!!

• Refer to the application at the beginning of the
  lesson. The American Heritage Center has a
  height of 77 ft. The area of the base is about
  38,000 square ft. Find the volume of air that
  the heating and cooling systems would have to be
  able to accommodate. Round to the nearest tenth.

V1/3Bh 1/3(38,000)(77) 975,333.3 ft cubed
The heating and cooling systems would have to
accommodate about 975,333 cubic feet of air.
4
Example 2

• Find the Volume of each solid. Round to the
  nearest tenth.
• A B

42
6 ft
14 cm
Use trigonometry to find the radius of the
base. Tan 42 6/r r6/tan 42 r is around
6.7 Now find the Volume V1/3Bh 1/3pie(6.7)squared
(6) 89.78pie 282.1ft cubed
8 cm
V1/3Bh 1/3(1/2Pa)h 1/3(1/2 . 48 . 4 3)
14 448 3 Around 776.cm cubed
5
Example 3
17 m

• Find the volume of the oblique pyramid at the
  right.
• First find the height of the pyramid.
• h squared 15 squared 17 squared
• h squared 64
• h 8
• Now find the area of the base.
• a squared 4 squared 15 squared
• a squared 209
• a square root 209
• Finally, find the volume.
• V 1/3Bh
• 1/3(1/2 . 8. 209) 8
• Around 154.2
• The volume is about 154.2 cubic meters.

8 m
15 m
15 m
15 m
a m
8 m
6
Assignment

• Page 618 11-21 odd