Transcript Document
10.3
There is a simple relationship between the volumes of prisms and pyramids with
congruent bases and the same height, and between cylinders and cones with
congruent bases and the same height.
Volume of Pyramid.
Volume of Cone.
JRLeon
Geometry Chapter 10.2
HGSH
10.3
Find the volume of a regular hexagonal pyramid with a height of 8 cm.
Each side of its base is 6 cm.
Find the area of the base.
𝟏
𝑩 = 𝒃𝒉 (𝒏)
𝟐
𝑩=
3 3
3
6
3
𝟏
(𝟔)(𝟑 𝟑)(𝟔)
𝟐
𝟏
𝑩 = (𝟑𝟔)(𝟑 𝟑)
𝟐
𝑩 = 𝟓𝟒 𝟑
Find the volume.
𝟏
V = 𝟑BH
JRLeon
𝟏
V = 𝟑 (𝟓𝟒 𝟑)(8)
Geometry Chapter 10.2
V = 𝟏𝟒𝟒 𝟑 𝒄𝒎𝟑
HGSH
10.4
JRLeon
Geometry Chapter 10.2
HGSH
10.4
JRLeon
Geometry Chapter 10.2
HGSH
10.5
What happens if you step into a bathtub that is filled to the brim? If you add a
scoop of ice cream to a glass filled with root beer? In each case, you’ll have a mess!
The volume of the liquid that overflows in each case equals the volume of the solid
below the liquid level. This volume is called an object’s displacement.
An important property of a material is its
density. Density is the mass of matter in a
given volume. You can find the mass of an
object by weighing it. You calculate density
by dividing the mass by the volume:
JRLeon
Geometry Chapter 10.5
HGSH
10.5
First, find the volume of
displaced water. Then divide
the mass by the volume to
get the density of the metal.
JRLeon
Geometry Chapter 10.5
HGSH
10.4
10.3 pg. 540: 2-10 even
10.4 pg. 548: 1-3
10.5 pg. 552 : 1-8
JRLeon
Geometry Chapter 10.2
HGSH