1. Volumes of Pyramids & Cones
Objectives:
1) Find the volume of a right Pyramid.
2) Find the volume of right Cone.

3. Finding Volumes of Pyramids and Cones
In Lesson 12.4, you learned that the volume of a prism is equal to Bh, where B is the area of the base, and h is the height.
From the figure at the left, it is clear that the volume of the pyramid with the same base area B and the same height h must be less than the volume of the prism.
The volume of the pyramid is one third the volume of the prism.

4. Vp = ⅓Bh I. Volume of a Pyramid
Pyramid – Is a polyhedron in which one face can be any polygon & the other faces are triangles.
Vp = ⅓Bh h
Area of the Base
A = l•w
A = ½bh
Height of the pyramid, not to be confused with the slant height (l)

5. Ex.1: Volume of a right Pyramid
Find the volume of a square pyramid with base edges of 10cm & a height of 20cm.
20cm
10cm
10cm

6. Ex.2: Another square pyramid
Find the area of a square pyramid w/ base edges 10ft long & a slant height 13ft.
V = (⅓)Bh
= (⅓) 100•h
= (⅓)100•___
= (⅓)1200
= 400ft3
a2 + b2 = c2
h = 132
h2 = 144
h = 12
13ft 12 h
5ft
10ft

7. Vc = ⅓Bh II. Volume of a Cone
Cone – Is “pointed” like a pyramid, but its base is a circle. h
Vc = ⅓Bh r
Area of the Base
A = r2

8. Ex.3: Find the volume of the following right cone w/ a diameter of 6in.
Circle
11in
3in

9. Ex.4: Volume of a Composite Figure
Volume of Cylinder NEXT!
V = Bh
= r2h
= (8)2(4)
= 256
10cm
4cm
8cm

10. Ex.5: Solve for the missing variable.
The following cone has a volume of 110. What is its radius.
V = ⅓Bh
V = ⅓(r2)h
110 = (⅓)r2(10)
110 = (⅓)r2(10)
11 = (⅓)r2
33 = r2
r = √33 cm
10cm r

11. Vc = ⅓Bh What have we learned??? Volume of Cones & Pyramids
Height is the actual height of the solid not the slant height!!!
Volume of Cones & Pyramids
Vc = ⅓Bh h
Area of Base h r