1 pizza box the surface area of a solid is the sum of the areas of its faces. the pizza box shown...
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Pizza Box The surface area of a solid is the sum of the areas of its faces. The pizza box shown has the shape of a rectangular prism. What is its surface area?
Surface Areas of Prisms and Cylinders10.5L
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In Example 1, a net is used to find the surface area of the pizza box. A net is a two-dimensional representation of a solid. The surface area of a solid is equal to the area of its net.
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Using a Net to Find Surface AreaEXAMPLE 1
The net at right represents the pizza box shown on the previous slide. (Any flaps or foldovers to hold the box together have been ignored.) Use the net to find the surface area of the pizza box.
ANSWER The surface area of the pizza box is 640 square inches.
Surface Areas of Prisms and Cylinders
SOLUTION
1 Find the area of each face.
Area of top or bottom: 16 • 16 = 256 in. 2
Area of each side: 16 • 2 = 32 in. 2
2 Find the sum of the areas of the faces.
256 + 256 + 32 + 32 + 32 + 32 = 640 in. 2
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Surface Areas of Prisms The lateral faces of a prism are the faces that are not bases. The lateral area of a prism is the sum of the areas of the lateral faces. The surface area of a prism is the sum of the areas of the bases and the lateral area. In the diagram, P is the base perimeter.
Surface Areas of Prisms and Cylinders
Surface area 2 • Base area Lateral area=
=
+
+
= +2B Ph
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Surface Areas of Prisms and Cylinders
Surface Area of a Prism
Words The surface area S of a prism is the sum of twice the base area B and the product of the base perimeter P and the height h.
Algebra S = 2B + Ph
Numbers S = 2(6 • 4) + [2(6) + 2(4)]10 = 248 square units
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Using a Formula to Find Surface AreaEXAMPLE 2
Find the surface area of the prism.
S = 2B + Ph Write formula for surface area.
Simplify.= 480
ANSWER The surface are of the prism is 480 square centimeters.
Substitute.
Surface Areas of Prisms and Cylinders
The bases of the prism are right triangles.
= 2( • 6 • 8) + (6 + 8 + 10)(18)12
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Surface Areas of Cylinders The curved surface of a cylinder is called the lateral surface. The lateral area of a cylinder is the area of the lateral surface. The surface area of a cylinder is the sum of the areas of the bases and the product of the base circumference and the height. In the diagram below, C represents the base circumference.
Surface Areas of Prisms and Cylinders
Surface area 2 • Base area Lateral area=
=
+
+
= +2B Ch
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Surface Areas of Prisms and Cylinders
Surface Area of a Cylinder
Words The surface area S of a cylinder is the sum of twice the base area B and the product of the base circumference C and the height h.
Algebra S = 2B + Ch = 2πr 2 + 2πrh
Numbers S = 2π(4) 2 + 2π(4)(10) ≈ 352 square units
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Using a Formula to Find Surface AreaEXAMPLE 3
Write formula for surface area of a cylinder.
= 2π(1.25) 2 + 2π(1.25)(5)
S = 2πr 2 + 2πrh
= 15.625π Simplify.
≈ 49.1
ANSWERThe surface area of the container of racquetballs is about 49 square inches.
Substitute.
Evaluate. Use a calculator.
Surface Areas of Prisms and Cylinders
Racquetball Find the surface area of the container of racquetballs. Round to the nearest square inch.
SOLUTIONThe radius is one half of the diameter, so r = 1.25 inches.
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