lasav of prisms and cylindersupdated
TRANSCRIPT
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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
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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
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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.
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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
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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
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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.
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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.
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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.
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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!
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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.
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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
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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.
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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
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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?
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Holt McDougal Geometry
10-4 Surface Area of Prisms and Cylinders
Example 5 Continued
Pup tent:
Tunnel tent:
The tunnel tent requires less nylon.
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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.