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

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?

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 Surface Area of Prisms, Cylinders, and Spheres

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 Surface Area of Prisms, Cylinders, and Spheres

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 Surface Area of Prisms, Cylinders, and Spheres

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 = S = 606 The surface area of the prism is 606 in 2. Multiply. Add. Course Surface Area of Prisms, Cylinders, and Spheres

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 = 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 Surface Area of Prisms, Cylinders, and Spheres 4 in.

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

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 Surface Area of Prisms, Cylinders, and Spheres

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 Surface Area of Prisms, Cylinders, and Spheres

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  S  S  The surface area of the cylinder is about ft 2. Multiply. Add. Round. Course Surface Area of Prisms, Cylinders, and Spheres

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  S  1, 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 Surface Area of Prisms, Cylinders, and Spheres

Lesson Quiz Find the surface area of each figure to the nearest tenth ft 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 Course Surface Area of Prisms, Cylinders, and Spheres