Students will be able to solve for perimeter, area and volume by….

1. Finding the Perimeter & Area of Rectangles & Parallelograms

2. Finding the Perimeter and Area of Triangles and Trapezoids

3. Solving Right Triangles using the Pythagorean Theorem

4. Finding the Circumference and Area of Circles

5. Understanding How to Draw Three-Dimensional Figures

6. Finding the Volume of Prisms and Cylinders

7. Finding the Volume of Pyramids and Cones

8. Finding the Surface Area of Prisms and Cylinders

9. Finding the Surface Area of Pyramids and Cones

10. Finding the Volume and Surface Area of Spheres

Pre-Algebra

6-8 Surface Area of Prisms and Cylinders

Review Pre-Algebra HW

Page 310 #8-12And

Page 314 #1-6

Pre-Algebra

6-8 Surface Area of Prisms and Cylinders

Rocky Loves Surface Area!Zach’s

Pet

Lizard!

Pre-Algebra

6-8 Surface Area of Prisms and Cylinders

Pre-Algebra HOMEWORK

Page 318

#1-8

SHOW WORK!

Pre-Algebra

6-8 Surface Area of Prisms and Cylinders

Learning Goal Assignment

Learn to find the surface area of prisms and cylinders.

Pre-Algebra

6-8 Surface Area of Prisms and Cylinders6-8 Surface Area of Prisms and Cylinders

Pre-Algebra

Warm Up

Problem of the Day

Lesson Presentation

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 .

3 m3

167 cm3

Pre-Algebra

6-8 Surface Area of Prisms and Cylinders

Pre-Algebra

6-8 Surface Area of Prisms and Cylinders

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

Pre-Algebra

6-8 Surface Area of Prisms and Cylinders

Learning Goal Assignment

Learn to find the surface area of prisms and cylinders.

Pre-Algebra

6-8 Surface Area of Prisms and Cylinders

Vocabulary

surface arealateral facelateral surface

Pre-Algebra

6-8 Surface Area of Prisms and Cylinders

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.

Pre-Algebra

6-8 Surface Area of Prisms and Cylinders

Surface Area Formula for a Rectangular Prism

Pre-Algebra

6-8 Surface Area of Prisms and Cylinders

Surface Area Formula for Cylinders

Pre-Algebra

6-8 Surface Area of Prisms and Cylinders

Pre-Algebra

6-8 Surface Area of Prisms and Cylinders

A. S = 2r2 + 2rh

= 2(42) + 2(4)(6)

= 80 in2 251.2 in2

B. S = 2B + Ph

= 204 ft2

= 2( • 8 • 3) + (18)(10)12

Additional Example 1: Finding Surface Area

Find the surface area of each figure

Pre-Algebra

6-8 Surface Area of Prisms and Cylinders

A. S = 2r2 + 2rh

= 2(152) + 2(15)(3)

= 540 in2 1695.6 cm2

B. S = 2B + Ph

= 252 cm2

= 2( • 7 • 6) + (21)(10)12

Try This: Example 1

Find the surface area of each figure 15 cm

3 cm

7 cm7 cm

7 cm10 cm

6 cm

Pre-Algebra

6-8 Surface Area of Prisms and CylindersAdditional 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.

Pre-Algebra

6-8 Surface Area of Prisms and Cylinders

Try This: Example 2

Original Dimensions Double the Height Double the Radius

S = 2r² + 2rh

= 2(3)2 + 2(3)(2)

= 30in2 ≈ 94.2 in2

S = 2r2 + 2r(2h)

= 2(3)2 + 2(3)(4)

= 42in2 ≈ 131.88 in2

S = 2r2 + 2(2r)h

= 2(6) 2 + 2(3)(2)

= 84in2 ≈ 263.76 in2

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.

They would not have the same effect. Doubling the radius would increase the surface area more than doubling the height.

Pre-Algebra

6-8 Surface Area of Prisms and Cylinders

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.

The diameter is 7.6 cm, so r = 3.8 cm.

L = 2rh

= 2(3.8)(11.2)

≈ 267.3 cm2

Pre-Algebra

6-8 Surface Area of Prisms and Cylinders

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?

The diameter is 6 ft, so r = 3 ft.

S = 2r2 + 2rh

= 2(32) + 2(3)(12)

≈ 282.6 ft2Move the decimal point 2 places to the left to divide by 100.

≈ 2.826 gal

Pre-Algebra

6-8 Surface Area of Prisms and Cylinders

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?

Lesson QuizFind the surface area of each figure to the nearest tenth. Use 3.14 for .

1. the triangular prism

2. the cylinder320.3 in2

360 cm2

84 in2