Holt McDougal Geometry

10-4 Surface Area of Prisms and Cylinders10-4 Surface Area of Prisms and Cylinders

Holt Geometry

Warm UpWarm UpLesson PresentationLesson PresentationLesson QuizLesson Quiz

Holt McDougal Geometry

Holt McDougal Geometry

10-4 Surface Area of Prisms and Cylinders

Warm UpFind the perimeter and area ofeach polygon.

1. a rectangle with base 14 cm and height 9 cm

2. a right triangle with 9 cm and 12 cm legs

3. an equilateral triangle with side length 6 cm

P = 46 cm; A = 126 cm2

P = 36 cm; A = 54 cm2

Holt McDougal Geometry

10-4 Surface Area of Prisms and Cylinders

Learn and apply the formula for the surface area of a prism.Learn and apply the formula for the surface area of a cylinder.

Objectives

Holt McDougal Geometry

10-4 Surface Area of Prisms and Cylinders

lateral facelateral edgeright prismoblique prismaltitudesurface arealateral surfaceaxis of a cylinderright cylinderoblique cylinder

Vocabulary

Holt McDougal Geometry

10-4 Surface Area of Prisms and Cylinders

Parts of a prism!

Holt McDougal Geometry

10-4 Surface Area of Prisms and CylindersAn altitude of a prism or cylinder is a perpendicular segment joining the planes of the bases. The height of a three-dimensional figure is the length of an altitude.Surface area is the total area of all faces and curvedsurfaces of a three-dimensional figure. The lateralarea of a prism is the sum of the areas of the lateral faces.

Holt McDougal Geometry

10-4 Surface Area of Prisms and CylindersThe net of a right prism can be drawn so that the lateral faces form a rectangle with the same height as the prism. The base of the rectangle is equal to theperimeter of the base of the prism.

Holt McDougal Geometry

10-4 Surface Area of Prisms and Cylinders

The surface area of a right rectangular prism with length ℓ, width w, and height h can be written asS = 2ℓw + 2wh + 2ℓh.FORMULA ON THE STATE ASSESSMENT!!!

All other prisms:

SA = Ph + 2B

P = Perimeter of the baseB = Base Area

Holt McDougal Geometry

10-4 Surface Area of Prisms and Cylinders

The surface area formula is only true for right prisms. To find the surface area of an oblique prism, add the areas of the faces.

Caution!

Holt McDougal Geometry

10-4 Surface Area of Prisms and CylindersExample 1A: Finding Lateral Areas and Surface Areas of

PrismsFind the lateral area and surface area of the right rectangular prism. Round to the nearest tenth, if necessary.

L = Ph = 32(14) = 448 ft2

S = Ph + 2B = 448 + 2(7)(9) = 574 ft2

P = 2(9) + 2(7) = 32 ft

Holt McDougal Geometry

10-4 Surface Area of Prisms and CylindersExample 1B: Finding Lateral Areas and Surface Areas of

PrismsFind the lateral area and surface area of a right regular triangular prism with height 20 cm and base edges of length 10 cm. Round to the nearest tenth, if necessary.L = Ph = 30(20) = 600 cm2

S = Ph + 2BP = 3(10) = 30 cm

The base area is

Holt McDougal Geometry

10-4 Surface Area of Prisms and CylindersWarm Up

Find the lateral area and surface area of a cube with edge length 8 cm.

L = Ph = 32(8) = 256 cm2

S = Ph + 2B = 256 + 2(8)(8) = 384 cm2

P = 4(8) = 32 cm

Holt McDougal Geometry

10-4 Surface Area of Prisms and CylindersRight and oblique Cylinders!

Holt McDougal Geometry

10-4 Surface Area of Prisms and Cylinders

Holt McDougal Geometry

10-4 Surface Area of Prisms and CylindersExample 2A: Finding Lateral Areas and Surface Areas of

Right CylindersFind the lateral area and surface area of the right cylinder. Give your answers in terms of .

L = 2rh = 2(8)(10) = 160 in2

The radius is half the diameter, or 8 in.

S = L + 2r2 = 160 + 2(8)2 = 288 in2

Holt McDougal Geometry

10-4 Surface Area of Prisms and CylindersExample 2B: Finding Lateral Areas and Surface Areas of

Right CylindersFind the lateral area and surface area of a right cylinder with circumference 24 cm and a height equal to half the radius. Give your answers in terms of .Step 1 Use the circumference to find the radius.

C = 2r Circumference of a circle24 = 2r Substitute 24 for C.

r = 12 Divide both sides by 2.

Holt McDougal Geometry

10-4 Surface Area of Prisms and CylindersExample 2B Continued

Step 2 Use the radius to find the lateral area and surface area. The height is half the radius, or 6 cm.

L = 2rh = 2(12)(6) = 144 cm2

S = L + 2r2 = 144 + 2(12)2 = 432 in2

Lateral area

Surface area

Find the lateral area and surface area of a right cylinder with circumference 24 cm and a height equal to half the radius. Give your answers in terms of .

Holt McDougal Geometry

10-4 Surface Area of Prisms and CylindersExample 3: Finding Surface Areas of Composite Three-

Dimensional FiguresFind the surface area of composite figure.Can you see the two shapes?

Holt McDougal Geometry

10-4 Surface Area of Prisms and CylindersExample 3 Continued

Two copies of the rectangular prism base are removed. The area of the base is B = 2(4) = 8 cm2.

The surface area of the rectangular prism is

.

.

A right triangular prism is added to the rectangular prism. The surface area of the triangular prism is

Holt McDougal Geometry

10-4 Surface Area of Prisms and Cylinders

The surface area of the composite figure is the sum of the areas of all surfaces on the exterior of the figure.

Example 3 Continued

S = (rectangular prism surface area) + (triangular prism surface area) – 2(rectangular prism base area)S = 52 + 36 – 2(8) = 72 cm2

Holt McDougal Geometry

10-4 Surface Area of Prisms and CylindersCheck It Out! Example 3

Find the surface area of the composite figure. Round to the nearest tenth.

Holt McDougal Geometry

10-4 Surface Area of Prisms and CylindersCheck It Out! Example 3 Continued

Find the surface area of the composite figure. Round to the nearest tenth.The surface area of the rectangular prism is

S =Ph + 2B = 26(5) + 2(36) = 202 cm2.

The surface area of the cylinder isS =Ph + 2B = 2(2)(3) + 2(2)2 = 20 ≈ 62.8 cm2.

The surface area of the composite figure is the sum of the areas of all surfaces on the exterior of the figure.

Holt McDougal Geometry

10-4 Surface Area of Prisms and Cylinders

S = (rectangular surface area) + (cylinder surface area) – 2(cylinder base area)

S = 202 + 62.8 — 2()(22) = 239.7 cm2

Check It Out! Example 3 Continued

Find the surface area of the composite figure. Round to the nearest tenth.

Holt McDougal Geometry

10-4 Surface Area of Prisms and Cylinders

Always round at the last step of the problem. Use the value of given by the key on your calculator.

Remember!

Holt McDougal Geometry

10-4 Surface Area of Prisms and CylindersExample 4: Exploring Effects of Changing Dimensions CUBE FORMULA! SA = 6s2 Volume = s3

How will the surface area change if the sides are tripled?

Holt McDougal Geometry

10-4 Surface Area of Prisms and CylindersExample 4 Continued

original dimensions: edge length tripled:

Notice than 3456 = 9(384). If the length, width, and height are tripled, the surface area is multiplied by 32, or 9.

S = 6ℓ2

= 6(8)2 = 384 cm2

S = 6ℓ2

= 6(24)2 = 3456 cm2

24 cm

Holt McDougal Geometry

10-4 Surface Area of Prisms and CylindersCheck It Out! Example 4

The height and diameter of the cylinder are

multiplied by . Describe the effect on the

surface area.

Holt McDougal Geometry

10-4 Surface Area of Prisms and Cylinders

original dimensions: height and diameter halved:S = 2(112) + 2(11)(14) = 550 cm2

S = 2(5.52) + 2(5.5)(7) = 137.5 cm2

11 cm

7 cm

Check It Out! Example 4 Continued

Notice than 550 = 4(137.5). If the dimensions are halved, the surface area is multiplied by

Holt McDougal Geometry

10-4 Surface Area of Prisms and CylindersExample 5: Recreation Application

A sporting goods company sells tents in two styles, shown below. The sides and floor of each tent are made of nylon.

Which tent requires less nylon to manufacture?

Holt McDougal Geometry

10-4 Surface Area of Prisms and CylindersExample 5 Continued

Pup tent:

Tunnel tent:

The tunnel tent requires less nylon.

Holt McDougal Geometry

10-4 Surface Area of Prisms and CylindersWarm Up

Find the lateral area and the surface area of each figure. Round to the nearest tenth, if necessary.

1. a cube with edge length 10 cm

2. a regular hexagonal prism with height 15 in. and base edge length 8 in.

L = 400 cm2 ; S = 600 cm2

L = 720 in2; S 1052.6 in2

Holt McDougal Geometry

10-4 Surface Area of Prisms and CylindersLesson Quiz: Part II

4. A cube has edge length 12 cm. If the edge length of the cube is doubled, what happens to the surface area?

5. Find the surface area of the composite figure.The surface area is multiplied by 4.

S = 3752 m2

Holt McDougal Geometry

10-4 Surface Area of Prisms and Cylinders