1. Students will be able to solve for perimeter, area and volume by….
Finding the Perimeter & Area of Rectangles & Parallelograms
Finding the Perimeter and Area of Triangles and Trapezoids
Solving Right Triangles using the Pythagorean Theorem
Finding the Circumference and Area of Circles
Understanding How to Draw Three-Dimensional Figures
Finding the Volume of Prisms and Cylinders
Finding the Volume of Pyramids and Cones
Finding the Surface Area of Prisms and Cylinders
Finding the Surface Area of Pyramids and Cones
Finding the Volume and Surface Area of Spheres

2. Review Pre-Algebra HW
Page 310 #8-12
And
Page 314 #1-6

3. Rocky Loves Surface Area!
Zach’s Pet Lizard!

4. Pre-Algebra HOMEWORK
Page 318 #1-8 SHOW WORK!

5. Learning Goal Assignment
Learn to find the surface area of prisms and cylinders.

6. 6-8 Surface Area of Prisms and Cylinders Warm Up Problem of the Day
Lesson Presentation
Pre-Algebra

7. 6-8 Surface Area of Prisms and Cylinders Warm Up 3 m3 167 cm3
Pre-Algebra
6-8
Surface Area of Prisms and Cylinders
Warm Up
1. A triangular pyramid has a base area of 1.2 m2 and a height of 7.5 m. What is the volume of the pyramid?
2. A cone has a radius of 4 cm and a height of 10 cm. What is the volume of the cone to the nearest cubic centimeter? Use 3.14 for p.
3 m3
167 cm3

8. Problem of the Day
An ice cream cone is filled halfway to the top. The radius of the filled part is half the radius at the top. What fraction of the cone’s volume is filled? 1 8

9. Learning Goal Assignment
Learn to find the surface area of prisms and cylinders.

10. Vocabulary
surface area
lateral face
lateral surface

11. Surface area is the sum of the areas of all surfaces of a figure
Surface area is the sum of the areas of all surfaces of a figure. The lateral faces of a prism are parallelograms that connect the bases. The lateral surface of a cylinder is the curved surface.

12. Surface Area Formula for a Rectangular Prism

13. Surface Area Formula for Cylinders

15. Additional Example 1: Finding Surface Area
Find the surface area of each figure
A. S = 2pr2 + 2prh
= 2p(42) + 2p(4)(6)
= 80p in2  in2
B. S = 2B + Ph
= 2( • 8 • 3) + (18)(10) 1 2
= 204 ft2

16. A. S = 2pr2 + 2prh = 2p(152) + 2p(15)(3) = 540p in2  1695.6 cm2
Try This: Example 1
Find the surface area of each figure
15 cm
A. S = 2pr2 + 2prh
3 cm
= 2p(152) + 2p(15)(3)
= 540p in2  cm2
7 cm
7 cm
6 cm
B. S = 2B + Ph
= 2( • 7 • 6) + (21)(10) 1 2
10 cm
7 cm
= 252 cm2

17. Additional Example 2: Exploring the Effects of Changing Dimensions
A cylinder has diameter 8 in. and height 3 in. Explain whether tripling the height would have the same effect on the surface area as tripling the radius.
They would not have the same effect. Tripling the radius would increase the surface area more than tripling the height.

18. Try This: Example 2
A cylinder has diameter 6 in. and height 2 in. Explain whether doubling the height would have the same effect on the surface area as doubling the radius.
Original Dimensions
Double the Height
Double the Radius
S = 2pr2 + 2pr(2h)
S = 2pr² + 2prh
S = 2pr2 + 2p(2r)h
= 2p(3)2 + 2p(3)(4)
= 2p(3)2 + 2p(3)(2)
= 2p(6) 2 + 2p(3)(2)
= 30p in2 ≈ 94.2 in2
= 42p in2 ≈ in2
= 84p in2 ≈ in2
They would not have the same effect. Doubling the radius would increase the surface area more than doubling the height.

19. Additional Example 3: Application
A cylindrical soup can is 7.6 cm in diameter and 11.2 cm tall. What is the area of the label that covers the side of the can?
Only the lateral surface needs to be covered.
L = 2rh
= 2(3.8)(11.2)
The diameter is 7.6 cm, so r = 3.8 cm.
≈ cm2

20. S = 2r2 + 2rh = 2(32) + 2(3)(12) Try This: Example 3
A cylindrical storage tank that is 6 ft in diameter and 12 ft tall needs to be painted. The paint will cover 100 square feet per gallon. How many gallons will it take to paint the tank?
S = 2r2 + 2rh
The diameter is 6 ft, so r = 3 ft.
= 2(32) + 2(3)(12)
≈ ft2
Move the decimal point 2 places to the left to divide by 100.
≈ gal

21. Lesson Quiz
Find the surface area of each figure to the nearest tenth. Use 3.14 for p.
1. the triangular prism
2. the cylinder
360 cm2
320.3 in2
3. All outer surfaces of a box are covered with gold foil, except the bottom. The box measures 6 in. long, 4 in. wide, and 3 in. high. How much gold foil was used?
84 in2