Presentation is loading. Please wait.

Presentation is loading. Please wait.

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.

Similar presentations


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 186.7 ft 3 12.6 ft 3 33.5 ft 3 162 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 2 9-4 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 2 9-4 Surface Area of Prisms, Cylinders, and Spheres

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

5 Vocabulary net surface area Insert Lesson Title Here Course 2 9-4 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 2 9-4 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 2 9-4 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 2 9-4 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 = 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

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 = 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.

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 2 9-4 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 2 9-4 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  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

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  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

15 Unlike the surface of a prism or a cylinder, the surface of a sphere cannot be flattened without stretching or shrinking. Course 2 9-4 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 2 9-4 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  803.84 S  803.8 The surface area of the sphere is about 803.8 m 2. Use the formula. Substitute. Multiply. Round. Course 2 9-4 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  452.16 S  452.2 The surface area of the sphere is about 452.2 in 2. Use the formula. Substitute. Multiply. Round. Try This: Example 3 6 in. Course 2 9-4 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 100.5 ft 2 352.0 ft 2 Insert Lesson Title Here 452.2 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. 1.2. Course 2 9-4 Surface Area of Prisms, Cylinders, and Spheres


Download ppt "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."

Similar presentations


Ads by Google