Download Lesson 8.7 File

Lesson 8.7: Surface Area
In this lesson you will:
 learn how to find the surface area of prisms, pyramids, cylinders, and cones
In Lesson 8.3, you calculated the surface area of walls and decks. But not all building
surfaces are quadrilaterals. How would you calculate the amount of glass necessary to
cover a pyramid-shaped building? Or the number of tiles needed to cover a coneshaped roof?
In this lesson, you will learn to how to find the surface area of prisms, pyramids,
cylinders, and cones. The surface area of each of these solids is the ______ of the
areas of all the faces or surfaces that enclose the solid. For prisms and pyramids, the
faces include the bases and its lateral faces.
*Add “surface area,” “base of a solid,” and “lateral face” to your vocabulary list.
In a prism, the bases are two ______________ polygons and the lateral faces are
rectangles or other parallelograms. In a pyramid, the base can be any polygon. The
lateral faces are ______________.
To find the surface areas of prisms and pyramids, follow these steps:
Steps for Finding Surface Area:
1. Draw and label each face of the solid as if you had _____ the solid apart along
its edges and laid it flat. Label the _______________.
2. Calculate the area of each _______. If some faces are identical, you only need
to find the area of _____.
3. Find the _______ area of all the faces.
Example 1: Find the surface area of the rectangular prism.
Example 2: Find the surface area of the cylinder.
The surface area of a pyramid is the area of the base plus the
areas of the triangular faces. The height of each triangular face is
called the _________ height. The slant height is labeled as l and
the pyramid height is labeled h.
*Add “slant height” to your vocabulary list.
Investigation 8.7.1: “Surface Area of a Regular Pyramid”
You can cut and unfold the surface area of a regular pyramid into these shapes.
A.) What is the area of each lateral face? A = ________
B.) What is the total lateral surface area? A = _________ What is the total lateral surface
area for any pyramid with a regular n-gon base? A = __________
C.) What is the area of the base for any regular n-gon pyramid? A = __________
D.) Use your expressions from parts B and C to write a formula for the surface area of a
regular n-gon pyramid in terms of n, base length b, slant height l, and apothem a.
A = _______________
E.) Write another expression for the surface area of a regular n-gon
pyramid in terms of slant height l, apothem a, and perimeter of
the base, P.
A = _______________
Investigation 8.7.2: “Surface Area of a Cone”
As the number of faces of a pyramid increases, it begins to look like a cone. You can think of
the lateral surface as many small triangles or as a sector of a circle.
A.) What is the area of the base? A = ________
B.) If you cut the lateral surface into many small triangles and then rearrange them into a
figure that resembles a parallelogram, how would you find the area? A = ________
C.) Based on your formulas for the base (part A) and for the lateral surface area (part B),
write a formula for the surface area of a cone. S.A.cone = _______________
Example 3: Find the total surface area of the cone.
Example 4: Find the surface area of this solid. D = 10 cm, d = 6 cm, h = 14 cm
(Hint: The surface area is the lateral surface area of the outside cylinder, plus the lateral
surface area of the inside cylinder, plus the area of the two bases, which are annuluses.)
ASSIGNMENT: ______________________________________________________