1. Volume of Pyramids and Cones
“If I had influence with the good fairy… I should ask that her gift to each child in the world be a sense of wonder so indestructible that it would last throughout life.”
Rachel Carson

2. Exit Activity
Table 2
Table 3
Table 4
Table 5
Table 6
Class
Triangular Prism
Rectangular Prism
Pentagonal Prism
Hexagonal Prism
Octagonal Prism
N-gonal Prism
Lateral Faces
Total Faces
Edges
Vertices
Volume Formula 3 4 5 6 8 n 5 6 7 8 10
n+2 9 12 15 18 24 3n 6 8 10 12 16 2n
(½ * b * h)H
(l*w)H
(½*a*s*5 )H
(½*a*s*6 )H
(½*a*s*8 )H
(½*P*a )H

3. Objectives Discover formulas for the volumes of pyramids and cones.
Practice three-dimensional visual thinking skills.

4. Pyramids and Cones
What do all these shapes have in common?

5. Investigation
The Volume Formulas for Pyramids and Cones p 522 Pyramid-Cone Volume Conjecture If B is the area of the base of a pyramid or a cone and H is the height of the solid, then the formula for the volume is V = ___________.
1 3 BH

6. Example
The shape to the left is a regular pentagonal pyramid. Find the volume of the shape.
Height = 8cm
6 cm

7. We must find the length of the apothem
Solution
We must find the length of the apothem
B = ½ * a *p
B = ½ * 3 (3)*(6)(5)
B = ½ * 3 (3)*30
B = 15* 3 (3)
B = 45 (3)
6cm
V = * B * H
3cm
3cm
V = * 45 (3) * 8
Apothem = 3(3)
V = 120(3) cm3

8. Example
What is the height of the cone to the left if the total volume is 324 in3.
Volume = 1 3 BH
Volume = 1 3 r2H
324 = 1 3 (92)H
324 = 27 * H
27 
12 = H H
9 in

9. Volume
What makes the volume of a cone and pyramid different from the volume of prisms and cylinders? How can we remember this difference?