This document discusses the volume formulas for pyramids and cones. It provides examples of calculating the volumes of different pyramids and cones using their base areas and heights. It also notes that tripling the height of a cone triples its volume, while tripling the radius increases the volume nine-fold.

1. 8-6 Volume of PyramidsHere Cones
Insert Lesson Title and 8-6 Volume of Pyramids and Cones
A pyramid is a three-dimensional figure whose base is a
VOLUME OF PYRAMIDS AND CONES
polygon, and all of the other faces are triangles.
It is named for the shape of its base.
A cone has a circular base. The height of a pyramid or cone
is measured from the highest point to the base along a
perpendicular line.
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8-6 Volume of Pyramids and Cones 8-6 Volume of Pyramids and Cones
Additional Example 1A: Finding the Volume of Additional Example 1B: Finding the Volume of
Pyramids and Cones Pyramids and Cones
Find the volume of the figure. Use 3.14 for !. Find the volume of the figure. Use 3.14 for !.
Area of the base
1
B = (4 • 7) = 14 cm2 B = !(32) = 9! in2
2
1 1 1 1
V= • 14 • 6 V= Bh V= • 9! • 10 V= Bh
3 3 3 3
Slant height-
the height of one of V = 28 cm3 V = 30! " 94.2 in3 Use 3.14 for !.
the sides. It’s
outside the pyramid.
Course 3 Course 3

2. 8-6 Volume of Pyramids and Cones 8-6 Volume of Pyramids and Cones
Find the volume of the figure. Use 3.14 for !. Check It Out: Example 1B
Find the volume of the figure. Use 3.14 for !.
Area of 1 face
1
B= (5 • 7) = 17.5 in2 B = !(32) = 9! m2
2
7 in. 7m
1 1 1 1
V= • 17.5 • 7 V= Bh V= • 9! • 7 V= Bh
3 3 3 3
5 in.
7 in. 3m
V " 40.8 in3 V = 21! " 65.9 m3 Use 3.14 for !.
Course 3 Course 3
8-6 Volume of Pyramids and Cones
Exploring the Effects of Changing Dimensions
A cone has a radius of 3 ft. and a height of 4 ft.
Explain whether tripling the height would have the
same effect on the volume of the cone as tripling the
radius.
*When the height of the cone is tripled, the volume is
tripled.
*When the radius is tripled, the volume becomes 9 times
the original volume.
Course 3