2. Lesson Menu 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

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

4. Key Concept

5. Example 1 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

6. Example 1 Surface Area of a Prism Answer: The lateral surface area is 336 square millimeters and the total surface area of the prism is 606 square millimeters. 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

7. Example 1 CYP A.28 yd 2 ; 108 yd 2 B.84 yd 2 ; 124 yd 2 C.84 yd 2 ; 164 yd 2 D.120 yd 2 ; 200 yd 2 Find the lateral and total surface areas of the rectangular prism.

8. Example 2 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. Surface Area of a Prism Estimate S.A. = (2 + 2 + 2)10 + (1)(2) or 61 in 2

9. Example 2 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 Surface Area of a Prism Area of Base

10. Example 2 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. Surface Area of a Prism Answer: The surface area is 46.95 square inches. Compare to the estimate.

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

12. Key Concept 3

13. Example 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  r 2 S.A. = 31.4 + 2  (2.5) 2 S.A. ≈ 70.7

14. 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.

15. Example 3 CYP A.219.9 cm 2 ; 377.0 cm 2 B.439.8 cm 2 ; 747.7 cm 2 C.1,539.4 cm 2 ; 1,693.3 cm 2 D.1,539.4 cm 2 ; 1,847.3 cm 2 Find the lateral area and the total surface area of the cylinder. Round to the nearest tenth.

16. Example 4 LABELS Find the area of the label on the can of juice. Round to the nearest tenth. Surface Area of a Cylinder 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 in 2

17. Example 4 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. Surface Area of a Cylinder Answer: The area of the label is about 113.1 square inches. Compare to the estimate.

18. Example 4 CYP A.212.1 cm 2 B.424.1 cm 2 C.487.7 cm 2 D.551.3 cm 2 LABELS Find the area of the label on the can of corn. Round to the nearest tenth.