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

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

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

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.

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

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.

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.

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

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 = 270 + 210 + 126 Multiply. S = 606 Add. The surface area of the prism is 606 in2.

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 = 48 + 24 + 36 Multiply. S = 108 Add. The surface area of the prism is 108 in2.

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, 2r, of the cylinder. So the area of the lateral surface is 2r. The area of each base is r2. r Circumference of cylinder (2r) h

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, 2r2, plus the area of its lateral surface, 2rh. S= 2r2 + 2rh

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 = 2r2 + 2rh Use the formula. S  (2 · 3.14 · 62) + (2 · 3.14 · 6 · 8.3) Substitute. S  226.08 + 312.744 Multiply. S  538.824 Add. S  538.8 Round. The surface area of the cylinder is about 538.8 ft2.

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 = 2r2 + 2rh Use the formula. S  (2 · 3.14 · 92) + (2 · 3.14 · 9 · 20) Substitute. S  508.68 + 1130.4 Multiply. S  1,639.08 Add. S  1,639.1 Round. The surface area of the cylinder is about 1,639.1 ft2.

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.

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= 4r2

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 = 4r2 Use the formula. S  4 · 3.14 · 82 Substitute. S  803.84 Multiply. S  803.8 Round. The surface area of the sphere is about 803.8 m2.

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 = 4r2 Use the formula. 6 in. S  4 · 3.14 · 62 Substitute. S  452.16 Multiply. S  452.2 Round. The surface area of the sphere is about 452.2 in2.

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