Surface Areas of Prisms, Cylinders,
9-4
and Spheres
Warm Up
Problem of the Day
Lesson Presentation
Course 2
Surface Area of Prisms, Cylinders, and
9-4 Spheres
Warm Up
Find the volume of each figure to the nearest
tenth. Use 3.14 for .
1. rectangular pyramid 7 ft by 8 ft by 10 ft tall
186.7 ft3
2. cone with radius 2 ft and height 3 ft 12.6 ft3
3. sphere with diameter 4 ft 33.5 ft3
4. triangular pyramid with base 54 ft2 and
height 9 ft 162 ft3
Course 2
Surface Area of Prisms, Cylinders, and
9-4 Spheres
Problem of the Day
When my age is divided by 2, 3, 4, or 6
there is always a remainder of 1, but
when it is divided by 7 there is no
remainder. How old am I?
49
Course 2
Surface Area of Prisms, Cylinders, and
9-4 Spheres
Learn to find the surface area of prisms,
cylinders, and spheres.
Course 2
Surface Area of Prisms, Cylinders, and
9-4 Spheres
Insert Lesson Title Here
Vocabulary
net
surface area
Course 2
Surface Area of Prisms, Cylinders, and
9-4 Spheres
If you remove the surface from a threedimensional figure and lay it out flat, the pattern
you make is called a net. You can construct nets
to cover almost any geometric solid.
Course 2
Surface Area of Prisms, Cylinders, and
9-4 Spheres
Since nets allow you to see all the surfaces of a
solid at one time, you can use them to help you
find the surface area of a three-dimensional figure.
Surface area is the sum of the areas of all
surfaces of a figure.
SURFACE AREA OF A POLYHEDRON
The surface area of a polyhedron is found by adding
the areas of each face of the polyhedron.
Course 2
Surface Area of Prisms, Cylinders, and
9-4 Spheres
You can use nets to write formulas for the
surface area of prisms. The surface area S is the
sum of the areas of the faces of the prism. For
the rectangular prism shown,
S = lw + lh + wh + lw + lh + wh
= 2lw + 2lh + 2wh
Top
w
Left
Right
h
l
Back
Front
Bottom
Course 2
Surface Area of Prisms, Cylinders, and
9-4 Spheres
Additional Example 1: Finding the Surface Area of a
Prism
Find the surface area
of the prism formed
by the net.
S = 2lw + 2lh + 2wh
S = (2 · 15 · 9) + (2 · 15 · 7) + (2 · 9 · 7) Substitute.
S = 270 + 210 + 126
Multiply.
S = 606
The surface area of the prism is 606 in2.
Add.
Course 2
Surface Area of Prisms, Cylinders, and
9-4 Spheres
Try This: Example 1
4 in.
Find the surface area
of the prism formed
by the net.
6 in.
3 in.
3 in.
4 in.
S = 2lw + 2lh + 2wh
S = (2 · 4 · 6) + (2 · 4 · 3) + (2 · 6 · 3)
Substitute.
S = 48 + 24 + 36
Multiply.
S = 108
The surface area of the prism is 108 in2.
Add.
Course 2
Surface Area of Prisms, Cylinders, and
9-4 Spheres
If you could remove the lateral surface from a
cylinder, like peeling a label from a can, you would
see that it has the shape of a rectangle when
flattened out.
You can draw a net for a cylinder by drawing the
circular bases (like the ends of a can) and the
rectangular lateral surface as shown below. The
length of the rectangle is the circumference, 2r, of
the cylinder. So the area of the lateral surface is 2r.
The area of each base is r2.
Circumference
r
of cylinder (2r)
h
Course 2
Surface Area of Prisms, Cylinders, and
9-4 Spheres
SURFACE AREA OF A CYLINDER
The surface area S of a cylinder is the sum of the
areas of its bases, 2r2, plus the area of its lateral
surface, 2rh.
S= 2r2 + 2rh
Course 2
Surface Area of Prisms, Cylinders, and
9-4 Spheres
Additional Example 2: Finding the Surface Area of a
Cylinder
Find the surface area of the cylinder formed
by the net to the nearest tenth. Use 3.14 for .
6 ft
8.3 ft
S = 2r2 + 2rh
6 ft
Use the formula.
S  (2 · 3.14 · 62) + (2 · 3.14 · 6 · 8.3)Substitute.
S  226.08 + 312.744
Multiply.
S  538.824
Add.
S  538.8
Round.
The surface area of the cylinder is about 538.8 ft2.
Course 2
Surface Area of Prisms, Cylinders, and
9-4 Spheres
Try This: Example 2
Find the surface area of the cylinder formed
by the net to the nearest tenth. Use 3.14 for .
9 ft
20 ft
S = 2r2 + 2rh
9 ft
Use the formula.
S  (2 · 3.14 · 92) + (2 · 3.14 · 9 · 20) Substitute.
S  508.68 + 1130.4
Multiply.
S  1,639.08
Add.
S  1,639.1
Round.
The surface area of the cylinder is about 1,639.1 ft2.
Course 2
Surface Area of Prisms, Cylinders, and
9-4 Spheres
Unlike the surface of a prism or a cylinder, the
surface of a sphere cannot be flattened without
stretching or shrinking.
Course 2
Surface Area of Prisms, Cylinders, and
9-4 Spheres
Because the surface of a sphere cannot be
flattened out, it is impossible to make a net for a
sphere. However, there is an exact formula for the
area of a sphere.
SURFACE AREA OF A CYLINDER
The surface area S of a sphere is 4 times  times
the radius r squared.
S= 4r2
Course 2
Surface Area of Prisms, Cylinders, and
9-4 Spheres
Additional Example 3: Finding the Surface Area of a
Sphere
Find the surface area of the sphere to the
nearest tenth. Use 3.14 for .
S = 4r2
S  4 · 3.14 · 82
S  803.84
S  803.8
Use the formula.
Substitute.
Multiply.
Round.
The surface area of the sphere is about 803.8 m2.
Course 2
Surface Area of Prisms, Cylinders, and
9-4 Spheres
Try This: Example 3
Find the surface area of the sphere to the
nearest tenth. Use 3.14 for .
6 in.
S = 4r2
S  4 · 3.14 · 62
S  452.16
S  452.2
Use the formula.
Substitute.
Multiply.
Round.
The surface area of the sphere is about 452.2 in2.
Course 2
Surface Area of Prisms, Cylinders, and
9-4 Spheres
Insert Lesson Title Here
Lesson Quiz
Find the surface area of each figure to the
nearest tenth.
1.
2.
352.0 ft2
100.5 ft2
3. a sphere with radius 6 ft 452.2 ft2
4. A drum is closed on the top and the bottom. The
diameter of the drum is 18 in. The height is 32 in.
Find the surface area. 2,317.3 in2
Course 2