1. 10.5 Surface Areas of Prisms and Cylinders Skill Check Skill Check Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation

2. 10.5 Surface Areas of Prisms and Cylinders Skill Check 1. length: 4 in., width: 7 in.28 in. 2 240 in. 2 1200 in. 2 13.75 in. 2 Find the area of a rectangle having the given length and width. 2. length: 12 in., width: 20 in. 3. length: 30 in., width: 40 in. 4. length: 2.5 in., width: 5.5 in.

3. 10.5 Surface Areas of Prisms and Cylinders 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. 10.5 Surface Areas of Prisms and Cylinders Using a Net to Find Surface Area EXAMPLE 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. 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

5. 10.5 Surface Areas of Prisms and Cylinders 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 areaLateral area = = + + = + 2B2BPh

6. 10.5 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

7. 10.5 Surface Areas of Prisms and Cylinders Using a Formula to Find Surface Area EXAMPLE 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. The bases of the prism are right triangles. = 2( 6 8) + (6 + 8 + 10)(18) 1 2

8. 10.5 Surface Areas of Prisms and Cylinders 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 areaLateral area = = + + = + 2B2BCh

9. 10.5 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

10. 10.5 Surface Areas of Prisms and Cylinders Using a Formula to Find Surface Area EXAMPLE 3 Write formula for surface area of a cylinder. = 2π(1.25) 2 + 2π(1.25)(5) S = 2πr 2 + 2πrh = 15.625π Simplify. ANSWER The surface area of the container of racquetballs is about 49 square inches. Substitute. Evaluate. Use a calculator. Racquetball Find the surface area of the container of racquetballs. Round to the nearest square inch. SOLUTION The radius is one half of the diameter, so r = 1.25 inches. 49.1

11. 10.5 Surface Areas of Prisms and Cylinders 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 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? 248 in. 2 2. A cylinder with radius 2 meters and height 14 meters 201 m 2 3. Find the lateral area of a pipe with diameter 6 feet and length 60 feet. Round to the nearest square foot. 1131 ft 2 about 12.6 in. 2