Bell Work:
Use substitution to solve for x
and y:
x – 2y = -1
2x – 3y = 4
Answer:
(11, 6)
Lesson 60:
Geometric Solids,
Prisms and Cylinders
In lesson 15 we defined a
geometric solid as a
geometric figure that has
three dimensions. Here are
some examples of
geometric solids.
Prism: a geometric solids
where two faces (bases) are
identical and parallel
polygons and where the
other faces are
parallelograms (lateral
faces)
Altitude*: in a prism it is a
perpendicular segment
joining the planes of the
bases.
The length of the altitude is
the height of the prism.
Right Prism*: a prism whose
lateral edges are at right
angles to the bases.
Note that in a right prism,
the lateral edges are also
altitudes.
Prisms are classified and
named according to the
shape of their bases.
A cylinder is like a prism except that
its base are closed curves instead of
polygons. The curved surface
between the base is called the
lateral surface. The segment joining
the centers of the bases is called
the axis of the cylinder. The altitude
of a cylinder is a perpendicular
segment joining the planes of the
bases.
Note that in a right cylinder,
the axis is also its altitude.
The volume of a prism can be
easily computed given the
area of a base and the height.
Since a cylinder is like a prism,
the volume of a cylinder is
computed in the exact same
way as the volume of a prism.
Volume of prisms and
cylinders:
 The volume of a prism or a
cylinder is equal to the
area of a base times the
height.
Example:
The area of a base of a
right pentagonal prism is
28 square cm and the
length of a lateral edge
is 10 cm. find the volume
of the right pentagonal
prism.
Answer:
Volume = (area of
2
base)(height)
= (28 cm3)(10 cm)
= 280 cm
We define the lateral surface
area of a prism or a cylinder to
be the area of all external
surfaces except the bases.
Unfortunately, there is no simple
way of computing lateral
surface areas of prisms or
cylinders unless they are right
prisms or right cylinders.
Lateral Surface Area of Right
Prisms and Right Cylinders:
 The lateral surface area of a
right prism or a right cylinder is
equal to the perimeter of a base
times the height.
To find the surface area of a
prism or a cylinder, we add
the areas of the bases to
the lateral surface area.
Example:
Find the lateral
surface area of this
right prism whose
bases are regular
pentagons.
Dimensions are in
meters.
15
8
Answer:
Lateral Surface Area =
(perimeter of base)(height)
= (40m)(15m)
2
= 600 meters
HW: Lesson 60 #1-30