1. 9-4 Surface Areas of Prisms, Cylinders, and Spheres Warm Up
Course 2
Warm Up
Problem of the Day
Lesson Presentation

2. 9-4 Surface Area of Prisms, Cylinders, and Spheres Warm Up
Course 2
9-4
Surface Area of Prisms, Cylinders, and 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

3. 9-4 Surface Area of Prisms, Cylinders, and Spheres Problem of the Day
Course 2
9-4
Surface Area of Prisms, Cylinders, and 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

4. 9-4 Learn to find the surface area of prisms, cylinders, and spheres.
Course 2
9-4
Surface Area of Prisms, Cylinders, and Spheres
Learn to find the surface area of prisms, cylinders, and spheres.

5. Insert Lesson Title Here
Course 2
9-4
Surface Area of Prisms, Cylinders, and Spheres
Insert Lesson Title Here
Vocabulary
net
surface area

6. 9-4 Surface Area of Prisms, Cylinders, and Spheres
Course 2
9-4
Surface Area of Prisms, Cylinders, and Spheres
If you remove the surface from a three-dimensional figure and lay it out flat, the pattern you make is called a net. You can construct nets to cover almost any geometric solid.

7. SURFACE AREA OF A POLYHEDRON
Course 2
9-4
Surface Area of Prisms, Cylinders, and 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.

8. 9-4 Surface Area of Prisms, Cylinders, and Spheres
Course 2
9-4
Surface Area of Prisms, Cylinders, and 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 h l
Left
Right
Back
Front
Bottom

9. Additional Example 1: Finding the Surface Area of a Prism
Course 2
9-4
Surface Area of Prisms, Cylinders, and 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 =
Multiply.
S = 606
Add.
The surface area of the prism is 606 in2.

10. 9-4 Surface Area of Prisms, Cylinders, and Spheres Try This: Example 1
Course 2
9-4
Surface Area of Prisms, Cylinders, and 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 =
Multiply.
S = 108
Add.
The surface area of the prism is 108 in2.

11. 9-4 Surface Area of Prisms, Cylinders, and Spheres
Course 2
9-4
Surface Area of Prisms, Cylinders, and 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. r
Circumference
of cylinder (2r) h

12. SURFACE AREA OF A CYLINDER
Course 2
9-4
Surface Area of Prisms, Cylinders, and 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

13. Additional Example 2: Finding the Surface Area of a Cylinder
Course 2
9-4
Surface Area of Prisms, Cylinders, and 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
6 ft
S = 2r2 + 2rh
Use the formula.
S  (2 · 3.14 · 62) + (2 · 3.14 · 6 · 8.3)
Substitute.
S 
Multiply.
S 
Add.
S  538.8
Round.
The surface area of the cylinder is about ft2.

14. 9-4 Surface Area of Prisms, Cylinders, and Spheres Try This: Example 2
Course 2
9-4
Surface Area of Prisms, Cylinders, and 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
9 ft
S = 2r2 + 2rh
Use the formula.
S  (2 · 3.14 · 92) + (2 · 3.14 · 9 · 20)
Substitute.
S 
Multiply.
S  1,639.08
Add.
S  1,639.1
Round.
The surface area of the cylinder is about 1,639.1 ft2.

15. 9-4 Surface Area of Prisms, Cylinders, and Spheres
Course 2
9-4
Surface Area of Prisms, Cylinders, and Spheres
Unlike the surface of a prism or a cylinder, the surface of a sphere cannot be flattened without stretching or shrinking.

16. SURFACE AREA OF A CYLINDER
Course 2
9-4
Surface Area of Prisms, Cylinders, and 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

17. Additional Example 3: Finding the Surface Area of a Sphere
Course 2
9-4
Surface Area of Prisms, Cylinders, and 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
Use the formula.
S  4 · 3.14 · 82
Substitute.
S 
Multiply.
S  803.8
Round.
The surface area of the sphere is about m2.

18. 9-4 Surface Area of Prisms, Cylinders, and Spheres Try This: Example 3
Course 2
9-4
Surface Area of Prisms, Cylinders, and Spheres
Try This: Example 3
Find the surface area of the sphere to the nearest tenth. Use 3.14 for .
S = 4r2
Use the formula.
6 in.
S  4 · 3.14 · 62
Substitute.
S 
Multiply.
S  452.2
Round.
The surface area of the sphere is about in2.

19. Insert Lesson Title Here
Course 2
9-4
Surface Area of Prisms, Cylinders, and Spheres
Insert Lesson Title Here
Lesson Quiz
Find the surface area of each figure to the nearest tenth.
3. a sphere with radius 6 ft 1. 2.
100.5 ft2
352.0 ft2
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