GEOMETRY: Chapter 12
12.2 Surface Area of Prisms
and Cylinders
A prism is a polyhedron with two congruent
faces, called bases, that lie in parallel planes.
Images taken from:
http://www.pinkmonkey.com/studyguides/subjects/geometry/chap8/g0808201.asp
The other faces, called lateral faces are
parallelograms formed by connecting the
corresponding vertices of the bases. The
segments connecting these vertices are
lateral edges. Prisms are classified by the
shapes of their bases.
Images taken from:
http://www.pinkmonkey.com/studyguides/subjects/geometry/chap8/g0808201.asp
The surface area of a polyhedron is the
sum of the areas of its faces. The lateral
area of a polyhedron is the sum of the
areas of its lateral faces.
Ex. 1
Find the surface area of a rectangular
prism with height 3 cm, length 6 cm, and
width 8 cm.
Answer: 180cm2
Right prisms: The height of a prism is the
perpendicular distance between its bases. In a
right prism, each lateral edge is
perpendicular to both bases.
Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 804.
A prism with lateral edges that are not
perpendicular to the bases is an oblique
prism.
Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 804.
Theorem 12.2: Surface Area of a Right Prism
The surface area S of a right prism is
S = 2B + Ph = aP + Ph,
where a is the apothem of the base, B is
the area of a base, P is the perimeter of a
base and h is the height.
Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 731.
Ex. 2. :Find the surface area of the right
hexagonal prism.
Answer: 1696.14ft2
Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 804.
A cylinder is a solid with congruent
circular bases that lie in parallel planes.
In a right cylinder, the segment joining
the centers of the bases is perpendicular
to the bases.
Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 805.
Surface Area of Right Cylinder
The surface area of a right cylinder is
Theorem 12.3:
Where B is the area of the base, C is the
circumference of the base, r is the radius of
the base, and h is the height.
Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 805.
Ex. 3
You are wrapping a poster in a cardboard cylinder.
The cylinder has a height of 36in. And a radius of
4 in. What is the minimum amount of cardboard
needed to cover the poster, including the two
bases of the cylinder?
Answer: at least 1005.3in2
Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 805.
Ex. 4
Find the height of the right cylinder, which has
a surface area of 262.64 cm2.
Answer: 7.2cm
Images taken from: Geometry. McDougal Littell: Boston, 2007. P. 806.
12.2, p. 731, #3-10 all, 13-15, 2027 all
(19 questions)