10.9 Surface Area
6.4.5 – I can find the surface areas of
prisms, pyramids, and cylinders
Warm Up
Identify the figure described.
1. two parallel congruent faces, with the
other faces being parallelograms
prism
2. a polyhedron that has a vertex and a
face at opposite ends, with the other
faces being triangles
pyramid
The surface area of a threedimensional figure is the sum of the
areas of its surfaces. To help you see
all the surfaces of a three-dimensional
figure, you can use a net. A net is the
pattern made when the surface of a
three-dimensional figure is laid out flat
showing each face of the figure.
What is the surface area of this
prism?
Find the surface area S of the prism.
Draw a net to help you see each face of the prism.
Use the formula A = lw to find the area of each face.
The surface area is 188 in2.
Find the surface area S of each prism.
Front: 9  7 = 63
63  2 = 126
Top:
9  5 = 45
45  2 = 90
Side:
7  5 = 35
35  2 = 70
S = 126 + 90 + 70 = 286 Add the areas of each face.
The surface area is 286 cm2.
6 in.
3 in.
11 in.
The surface area is 234 in2.
8 cm
6 cm
10 cm
The surface area is 376 cm2.
S = area of square + 4  (area of
triangular face)
The surface area is 161 ft2.
S = area of square + 4  (area of
triangular face)
10 ft
5 ft
5 ft
10 ft
5 ft
The surface area is 125 ft2.
The surface area of a cylinder equals the
sum of the area of its bases and the area
of its curved surface.
Helpful Hint
To find the area of the curved surface of a
cylinder, multiply its height by the
circumference of the base.
Surface Area of a Cylinder
A cylinder has a total of
three surfaces: a top,
bottom, and middle. The
top and bottom, which are
circles, are easy to
visualize. The area of a
circle is πr2
Find the surface area S of the cylinder.
Use 3.14 for , and round to the nearest
hundredth.
S = area of curved surface + 2  (area of each base)
The surface area is about 276.32
ft2.
Video
Find the surface area of each figure. Use
3.14 for .
1. rectangular prism with base length 6 ft, width
5 ft, and height 7 ft 214 ft2
2. cylinder with radius 3 ft and height 7 ft 188.4 ft2
3. Find the surface area of the figure shown.
208 ft2
2. Find the surface area of a cylinder with
radius 5 ft and height 8 ft. Use 3.14 for .
A. 576.8 ft2
B. 408.2 ft2
C. 376.2 ft2
D. 251.2 ft2
3. Find the surface area of the figure shown.
A. 162 ft2
B. 152 ft2
C. 142 ft2
D. 132 ft2
Square Pyramid
4.8 ft
5.6 ft
Triangular Prism
6 in
3 in
Cylinder
24 in
12 in
4 in