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9-4 Surface Areas of Prisms, Cylinders, and Spheres Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation.

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Presentation on theme: "9-4 Surface Areas of Prisms, Cylinders, and Spheres Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation."— Presentation transcript:

1 9-4 Surface Areas of Prisms, Cylinders, and Spheres Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

2 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 ft ft ft ft 3 2. cone with radius 2 ft and height 3 ft 3. sphere with diameter 4 ft 4. triangular pyramid with base 54 ft 2 and height 9 ft Course Surface Area of Prisms, Cylinders, and Spheres

3 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 Course Surface Area of Prisms, Cylinders, and Spheres

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

5 Vocabulary net surface area Insert Lesson Title Here Course Surface Area of Prisms, Cylinders, and Spheres

6 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

7 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

8 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

9 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

10 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.

11 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

12 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

13 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

14 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

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

16 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= 4r 2 Course Surface Area of Prisms, Cylinders, and Spheres

17 Find the surface area of the sphere to the nearest tenth. Use 3.14 for . Additional Example 3: Finding the Surface Area of a Sphere S = 4r 2 S  4 · 3.14 · 8 2 S  S  The surface area of the sphere is about m 2. Use the formula. Substitute. Multiply. Round. Course Surface Area of Prisms, Cylinders, and Spheres

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

19 Lesson Quiz Find the surface area of each figure to the nearest tenth. 3. a sphere with radius 6 ft ft ft 2 Insert Lesson Title Here ft 2 2,317.3 in 2 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 Course Surface Area of Prisms, Cylinders, and Spheres


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