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**9-4 Surface Areas of Prisms, Cylinders, and Spheres Warm Up**

Course 2 Warm Up Problem of the Day Lesson Presentation

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**9-4 Surface Area of Prisms, Cylinders, and Spheres Warm Up**

Course 2 9-4 Surface Area of Prisms, Cylinders, and Spheres Warm Up Find the volume of each figure to the nearest tenth. Use 3.14 for . 1. rectangular pyramid 7 ft by 8 ft by 10 ft tall 186.7 ft3 2. cone with radius 2 ft and height 3 ft 12.6 ft3 3. sphere with diameter 4 ft 33.5 ft3 4. triangular pyramid with base 54 ft2 and height 9 ft 162 ft3

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**9-4 Surface Area of Prisms, Cylinders, and Spheres Problem of the Day**

Course 2 9-4 Surface Area of Prisms, Cylinders, and Spheres Problem of the Day When my age is divided by 2, 3, 4, or 6 there is always a remainder of 1, but when it is divided by 7 there is no remainder. How old am I? 49

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**9-4 Learn to find the surface area of prisms, cylinders, and spheres.**

Course 2 9-4 Surface Area of Prisms, Cylinders, and Spheres Learn to find the surface area of prisms, cylinders, and spheres.

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**Insert Lesson Title Here**

Course 2 9-4 Surface Area of Prisms, Cylinders, and Spheres Insert Lesson Title Here Vocabulary net surface area

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**9-4 Surface Area of Prisms, Cylinders, and Spheres**

Course 2 9-4 Surface Area of Prisms, Cylinders, and Spheres 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.

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**SURFACE AREA OF A POLYHEDRON**

Course 2 9-4 Surface Area of Prisms, Cylinders, and Spheres 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. SURFACE AREA OF A POLYHEDRON The surface area of a polyhedron is found by adding the areas of each face of the polyhedron.

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**9-4 Surface Area of Prisms, Cylinders, and Spheres**

Course 2 9-4 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 w h l Left Right Back Front Bottom

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**Additional Example 1: Finding the Surface Area of a Prism**

Course 2 9-4 Surface Area of Prisms, Cylinders, and Spheres Additional Example 1: Finding the Surface Area of a Prism Find the surface area of the prism formed by the net. S = 2lw + 2lh + 2wh S = (2 · 15 · 9) + (2 · 15 · 7) + (2 · 9 · 7) Substitute. S = Multiply. S = 606 Add. The surface area of the prism is 606 in2.

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**9-4 Surface Area of Prisms, Cylinders, and Spheres Try This: Example 1**

Course 2 9-4 Surface Area of Prisms, Cylinders, and Spheres Try This: Example 1 4 in. Find the surface area of the prism formed by the net. 6 in. 3 in. 3 in. 4 in. S = 2lw + 2lh + 2wh S = (2 · 4 · 6) + (2 · 4 · 3) + (2 · 6 · 3) Substitute. S = Multiply. S = 108 Add. The surface area of the prism is 108 in2.

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**9-4 Surface Area of Prisms, Cylinders, and Spheres**

Course 2 9-4 Surface Area of Prisms, Cylinders, and Spheres 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, 2r, of the cylinder. So the area of the lateral surface is 2r. The area of each base is r2. r Circumference of cylinder (2r) h

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**SURFACE AREA OF A CYLINDER**

Course 2 9-4 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, 2r2, plus the area of its lateral surface, 2rh. S= 2r2 + 2rh

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**Additional Example 2: Finding the Surface Area of a Cylinder**

Course 2 9-4 Surface Area of Prisms, Cylinders, and Spheres Additional Example 2: Finding the Surface Area of a Cylinder Find the surface area of the cylinder formed by the net to the nearest tenth. Use 3.14 for . 6 ft 8.3 ft 6 ft S = 2r2 + 2rh Use the formula. S (2 · 3.14 · 62) + (2 · 3.14 · 6 · 8.3) Substitute. S Multiply. S Add. S 538.8 Round. The surface area of the cylinder is about ft2.

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**9-4 Surface Area of Prisms, Cylinders, and Spheres Try This: Example 2**

Course 2 9-4 Surface Area of Prisms, Cylinders, and Spheres Try This: Example 2 Find the surface area of the cylinder formed by the net to the nearest tenth. Use 3.14 for . 9 ft 20 ft 9 ft S = 2r2 + 2rh Use the formula. S (2 · 3.14 · 92) + (2 · 3.14 · 9 · 20) Substitute. S Multiply. S 1,639.08 Add. S 1,639.1 Round. The surface area of the cylinder is about 1,639.1 ft2.

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**9-4 Surface Area of Prisms, Cylinders, and Spheres**

Course 2 9-4 Surface Area of Prisms, Cylinders, and Spheres Unlike the surface of a prism or a cylinder, the surface of a sphere cannot be flattened without stretching or shrinking.

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**SURFACE AREA OF A CYLINDER**

Course 2 9-4 Surface Area of Prisms, Cylinders, and Spheres Because the surface of a sphere cannot be flattened out, it is impossible to make a net for a sphere. However, there is an exact formula for the area of a sphere. SURFACE AREA OF A CYLINDER The surface area S of a sphere is 4 times times the radius r squared. S= 4r2

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**Additional Example 3: Finding the Surface Area of a Sphere**

Course 2 9-4 Surface Area of Prisms, Cylinders, and Spheres Additional Example 3: Finding the Surface Area of a Sphere Find the surface area of the sphere to the nearest tenth. Use 3.14 for . S = 4r2 Use the formula. S 4 · 3.14 · 82 Substitute. S Multiply. S 803.8 Round. The surface area of the sphere is about m2.

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**9-4 Surface Area of Prisms, Cylinders, and Spheres Try This: Example 3**

Course 2 9-4 Surface Area of Prisms, Cylinders, and Spheres Try This: Example 3 Find the surface area of the sphere to the nearest tenth. Use 3.14 for . S = 4r2 Use the formula. 6 in. S 4 · 3.14 · 62 Substitute. S Multiply. S 452.2 Round. The surface area of the sphere is about in2.

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**Insert Lesson Title Here**

Course 2 9-4 Surface Area of Prisms, Cylinders, and Spheres Insert Lesson Title Here Lesson Quiz Find the surface area of each figure to the nearest tenth. 3. a sphere with radius 6 ft 1. 2. 100.5 ft2 352.0 ft2 452.2 ft2 4. 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. 2,317.3 in2

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