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Skill Check

Skill Check. Lesson Presentation. Lesson Quiz. Skill Check. Find the area of a rectangle having the given length and width. 1. length: 4 in., width: 7 in. 28 in. 2. 240 in. 2. 2. length: 12 in., width: 20 in. 1200 in. 2. 3. length: 30 in., width: 40 in. 13.75 in. 2.

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Skill Check

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  1. Skill Check Lesson Presentation Lesson Quiz

  2. Skill Check Find the area of a rectangle having the given length and width. 1. length: 4 in., width: 7 in. 28 in.2 240 in.2 2. length: 12 in., width: 20 in. 1200 in.2 3. length: 30 in., width: 40 in. 13.75 in.2 4. length: 2.5 in., width: 5.5 in.

  3. 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? 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.

  4. 1 EXAMPLE 2 1 Using a Net to Find Surface Area 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. SOLUTION 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 Find the sum of the areas of the faces. 256 + 256 + 32 + 32 + 32 + 32 = 640 in.2 ANSWER The surface area of the pizza box is 640 square inches.

  5. + 2B Ph = 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 area = 2 • Base area + Lateral area + =

  6. 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

  7. 2 EXAMPLE The bases of the prism are right triangles. 1 = 2( • 6 • 8) + (6 + 8 + 10)(18) 2 Using a Formula to Find Surface Area Find the surface area of the prism. S = 2B +Ph Write formula for surface area. Substitute. = 480 Simplify. ANSWER The surface are of the prism is 480 square centimeters.

  8. + 2B Ch = 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 area = 2 • Base area + Lateral area + =

  9. S = 2π(4)2 + 2π(4)(10) 352 square units 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 = 2πr2 + 2πrh Numbers

  10. 3 EXAMPLE 49.1 Using a Formula to Find Surface Area Racquetball Find the surface area of the container of racquetballs. Round to the nearest square inch. The radius is one half of the diameter, so r = 1.25 inches. SOLUTION S = 2πr2 + 2πrh Write formula for surface area of a cylinder. = 2π(1.25)2 + 2π(1.25)(5) Substitute. = 15.625π Simplify. Evaluate. Use a calculator. The surface area of the container of racquetballs is about 49 square inches. ANSWER

  11. Lesson Quiz Find the surface area of the solid. Round to the nearest whole number. 1. A rectangular prism with a height of 16 inches and a base of length 3 inches and width 4 inches 248 in.2 2. A cylinder with radius 2 meters and height 14 meters 201 m2 3. Find the lateral area of a pipe with diameter 6 feet and length 60 feet. Round to the nearest square foot. 1131 ft2 4. Challenge You have a cylindrical rod that has a radius of 1 inch and is 12 inches long. If you cut the rod into three pieces of the same size, by how much would the total surface area increase? about 12.6 in.2

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