1. Silently get started on the pink worksheet. Today’s Plan: -Warm-up -Surface Area LT: I will calculate the surface area of prisms. 04/19/11 Surface Area

2. LT: I will calculate the surface area of prism. Today’s Plan: -Warm-up -Surface Area LT: I will calculate the surface area of prisms. 04/19/11 Surface Area If this was folded back into a box what would the length, width, and height be?

3. If you remove the surface from a three- dimensional figure and lay it out flat, the pattern you make is called a net. You can construct nets to cover almost any geometric solid. Course 2 9-4 Surface Area of Prisms, Cylinders, and Spheres

4. SURFACE AREA OF A POLYHEDRON The surface area of a polyhedron is found by adding the areas of each face of the polyhedron. Since nets allow you to see all the surfaces of a solid at one time, you can use them to help you find the surface area of a three-dimensional figure. Surface area is the sum of the areas of all surfaces of a figure. Course 2 9-4 Surface Area of Prisms, Cylinders, and Spheres

5. You can use nets to write formulas for the surface area of prisms. The surface area S is the sum of the areas of the faces of the prism. For the rectangular prism shown, S = lw + lh + wh + lw + lh + wh = 2lw + 2lh + 2wh Top Bottom Front Back LeftRight w h l Course 2 9-4 Surface Area of Prisms, Cylinders, and Spheres

6. Find the surface area of the prism formed by the net. Additional Example 1: Finding the Surface Area of a Prism = 2lw + 2lh + 2wh S = (2 · 15 · 9) + (2 · 15 · 7) + (2 · 9 · 7) S Substitute. S = 270 + 210 + 126 S = 606 The surface area of the prism is 606 in 2. Multiply. Add. Course 2 9-4 Surface Area of Prisms, Cylinders, and Spheres

7. Find the surface area of the prism formed by the net. = 2lw + 2lh + 2wh S = (2 · 4 · 6) + (2 · 4 · 3) + (2 · 6 · 3) S Substitute. S = 48 + 24 + 36 S = 108 The surface area of the prism is 108 in 2. Multiply. Add. Try This: Example 1 4 in. 6 in. 3 in. Course 2 9-4 Surface Area of Prisms, Cylinders, and Spheres 4 in.

8. Assignment: MSP practice worksheet (2 4-step problems) And pg 489 #1,2,7,&8 (showing all work) Today’s Plan: -Warm-up -Surface Area LT: I will calculate the surface area of prisms. 04/19/11 Surface Area

9. If you could remove the lateral surface from a cylinder, like peeling a label from a can, you would see that it has the shape of a rectangle when flattened out. You can draw a net for a cylinder by drawing the circular bases (like the ends of a can) and the rectangular lateral surface as shown below. The length of the rectangle is the circumference, 2r, of the cylinder. So the area of the lateral surface is 2r. The area of each base is r 2. r Circumference of cylinder (2r) h Course 2 9-4 Surface Area of Prisms, Cylinders, and Spheres

10. SURFACE AREA OF A CYLINDER The surface area S of a cylinder is the sum of the areas of its bases, 2r 2, plus the area of its lateral surface, 2rh. S= 2r 2 + 2rh Course 2 9-4 Surface Area of Prisms, Cylinders, and Spheres

11. Find the surface area of the cylinder formed by the net to the nearest tenth. Use 3.14 for . Additional Example 2: Finding the Surface Area of a Cylinder 6 ft 8.3 ft S = 2r 2 + 2rh S  (2 · 3.14 · 6 2 ) + (2 · 3.14 · 6 · 8.3) Substitute. Use the formula. S  226.08 + 312.744 S  538.824 S  538.8 The surface area of the cylinder is about 538.8 ft 2. Multiply. Add. Round. Course 2 9-4 Surface Area of Prisms, Cylinders, and Spheres

12. Find the surface area of the cylinder formed by the net to the nearest tenth. Use 3.14 for . 9 ft 20 ft S = 2r 2 + 2rh S  (2 · 3.14 · 9 2 ) + (2 · 3.14 · 9 · 20) Substitute. Use the formula. S  508.68 + 1130.4 S  1,639.08 S  1,639.1 The surface area of the cylinder is about 1,639.1 ft 2. Multiply. Add. Round. Try This: Example 2 Course 2 9-4 Surface Area of Prisms, Cylinders, and Spheres

13. Lesson Quiz Find the surface area of each figure to the nearest tenth. 100.5 ft 2 352.0 ft 2 Insert Lesson Title Here 2,317.3 in 2 3. A drum is closed on the top and the bottom. The diameter of the drum is 18 in. The height is 32 in. Find the surface area. 1.2. Course 2 9-4 Surface Area of Prisms, Cylinders, and Spheres