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

Example 3: Finding Surface Areas of Composite Three-Dimensional Figures

Find the surface area of the composite figure.

Holt McDougal Geometry

10-4 Surface Area of Prisms and Cylinders

Example 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 Cylinders

Check 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 Cylinders

Check 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 is

S =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 Cylinders

Example 4: Exploring Effects of Changing Dimensions

The edge length of the cube is tripled. Describe the effect on the surface area.

Holt McDougal Geometry

10-4 Surface Area of Prisms and Cylinders

Example 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 Cylinders

Check 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 Cylinders

Example 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 Cylinders

Example 5 Continued

Pup tent:

Tunnel tent:

The tunnel tent requires less nylon.

Holt McDougal Geometry

10-4 Surface Area of Prisms and Cylinders

Check It Out! Example 5

A piece of ice shaped like a 5 cm by 5 cm by 1 cm rectangular prism has approximately the same volume as the pieces below. Compare the surface areas. Which will melt faster?

The 5 cm by 5 cm by 1 cm prism has a surface area of 70 cm2, which is greater than the 2 cm by 3 cm by4 cm prism and about the same as the half cylinder. It will melt at about the same rate as the half cylinder.