Surface Areas of Prisms and Cylinders 10.5 LESSON 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.
Surface Areas of Prisms and Cylinders 10.5 LESSON Surface Areas of Prisms and Cylinders EXAMPLE 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 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 ANSWER The surface area of the pizza box is 640 square inches.
Surface Areas of Prisms and Cylinders 10.5 LESSON 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 area + Lateral area = + 2B Ph = +
Surface Areas of Prisms and Cylinders 10.5 LESSON 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
Surface Areas of Prisms and Cylinders 10.5 LESSON Surface Areas of Prisms and Cylinders EXAMPLE 2 Using a Formula to Find Surface Area Find the surface area of the prism. The bases of the prism are right triangles. S = 2B + Ph Write formula for surface area. = 2( • 6 • 8) + (6 + 8 + 10)(18) 1 2 Substitute. = 480 Simplify. ANSWER The surface are of the prism is 480 square centimeters.
Surface Areas of Prisms and Cylinders 10.5 LESSON 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 area + Lateral area = + 2B Ch = +
Surface Areas of Prisms and Cylinders 10.5 LESSON 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
Surface Areas of Prisms and Cylinders 10.5 LESSON Surface Areas of Prisms and Cylinders EXAMPLE 3 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 = 2πr 2 + 2πrh Write formula for surface area of a cylinder. = 2π(1.25) 2 + 2π(1.25)(5) Substitute. = 15.625π Simplify. ≈ 49.1 Evaluate. Use a calculator. The surface area of the container of racquetballs is about 49 square inches. ANSWER