Main Idea and New Vocabulary Key Concept: Surface Area of a Prism Example 1: Surface Area of a Prism Example 2: Surface Area of a Prism Key Concept: Surface Area of a Cylinder Example 3: Surface Area of a Cylinder Example 4: Surface Area of a Cylinder Lesson Menu

Find the lateral and total surface area of prisms and cylinders. lateral face lateral surface area total surface area Main Idea/Vocabulary

Key Concept

Find the lateral and total surface areas of the rectangular prism. Surface Area of a Prism Find the lateral and total surface areas of the rectangular prism. Begin by finding the perimeter and area of one base. Perimeter of Base P = 2b + 2w P = 2(15) + 2(9) or 48 Area of Base B = bw B = (15)(9) or 135 Example 1

Use this information to find the lateral and total surface areas. Surface Area of a Prism Use this information to find the lateral and total surface areas. Lateral Surface Area L.A. = Ph L.A. = 48(7) or 336 Total Surface Area S.A. = L.A. + 2B S.A. = 336 + 2(135) or 606 Answer: The lateral surface area is 336 square millimeters and the total surface area of the prism is 606 square millimeters. Example 1

Find the lateral and total surface areas of the rectangular prism. A. 28 yd2; 108 yd2 B. 84 yd2; 124 yd2 C. 84 yd2; 164 yd2 D. 120 yd2; 200 yd2 Example 1 CYP

Estimate S.A. = (2 + 2 + 2)10 + (1)(2) or 61 in2 Surface Area of a Prism KALEIDOSCOPE A kaleidoscope is made of stained glass in the shape of a triangular prism. The bases are equilateral triangles. Find the total surface area. Estimate S.A. = (2 + 2 + 2)10 + (1)(2) or 61 in2 Example 2

Surface Area of a Prism The bases of the prism are triangles with side lengths of 1.5 inches, and a height of 1.3 inches. Find the perimeter and area of one base. Perimeter of Base P = 1.5 + 1.5 + 1.5 P = 4.5 Area of Base Example 2

Use this information to find the total surface area. Surface Area of a Prism Use this information to find the total surface area. S.A. = Ph + 2B Total surface area of prism S.A. = 4.5(10) + 2(0.975) P = 4.5, h = 10, and B = 0.975 S.A. = 46.95 Simplify. Answer: The surface area is 46.95 square inches. Compare to the estimate. Example 2

FURNITURE A corner cabinet is in the shape of a triangular prism FURNITURE A corner cabinet is in the shape of a triangular prism. The bases are right triangles. Find the total surface area. A. 2,016 in2 B. 2,310 in2 C. 2,604 in2 D. 7,056 in2 Example 2 CYP

Key Concept 3

Surface Area of a Cylinder Find the lateral area and the total surface area of the cylinder. Round to the nearest tenth. Since the diameter is 5 meters, the radius is 2.5 meters. Lateral Surface Area L.A. = 2rh L.A. = 2(2.5)(2) L.A. ≈ 31.4 Total Surface Area S.A. = L.A. + 2r2 S.A. = 31.4 + 2(2.5)2 S.A. ≈ 70.7 Example 3

Surface Area of a Cylinder Answer: The lateral area is about 31.4 square meters and the surface area of the cylinder is about 70.7 square meters. Example 3

Find the lateral area and the total surface area of the cylinder Find the lateral area and the total surface area of the cylinder. Round to the nearest tenth. A. 219.9 cm2; 377.0 cm2 B. 439.8 cm2; 747.7 cm2 C. 1,539.4 cm2; 1,693.3 cm2 D. 1,539.4 cm2; 1,847.3 cm2 Example 3 CYP

Surface Area of a Cylinder LABELS Find the area of the label on the can of juice. Round to the nearest tenth. Since the label covers the lateral surface of the can, you only need to find the can’s lateral surface area. Estimate L.A. = 2rh L.A. ≈ 2(3)(2)(8)  ≈ 3, r = 2.25 ≈ 2, h = 8 L.A. ≈ 96 in2 Example 4

Surface Area of a Cylinder L.A. = 2rh Lateral surface area of cylinder L.A. = 2(2.25)(8) r = 2.25, h = 8 L.A. ≈ 113.1 Simplify. Answer: The area of the label is about 113.1 square inches. Compare to the estimate. Example 4

LABELS Find the area of the label on the can of corn LABELS Find the area of the label on the can of corn. Round to the nearest tenth. A. 212.1 cm2 B. 424.1 cm2 C. 487.7 cm2 D. 551.3 cm2 Example 4 CYP