Surface Areas of Prisms Cylinders 9 4 and

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

Surface Area of Prisms, Cylinders, and 9 -4 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 ft 3 2. cone with radius 2 ft and height 3 ft 12. 6 ft 3 3. sphere with diameter 4 ft 33. 5 ft 3 4. triangular pyramid with base 54 ft 2 and height 9 ft 162 ft 3 Course 2

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

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

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

Surface Area of Prisms, Cylinders, and 9 -4 Spheres If you remove the surface from a threedimensional 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

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

Surface Area of Prisms, Cylinders, and 9 -4 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 = 2 lw + 2 lh + 2 wh Top w Left Right h l Back Front Bottom Course 2

Surface Area of Prisms, Cylinders, and 9 -4 Spheres Additional Example 1: Finding the Surface Area of a Prism Find the surface area of the prism formed by the net. S = 2 lw + 2 lh + 2 wh S = (2 · 15 · 9) + (2 · 15 · 7) + (2 · 9 · 7) Substitute. S = 270 + 210 + 126 Multiply. S = 606 The surface area of the prism is 606 in 2. Add. Course 2

Surface Area of Prisms, Cylinders, and 9 -4 Spheres Try This: Example 1 4 in. Find the surface area of the prism formed by the net. 6 in. 3 in. 4 in. S = 2 lw + 2 lh + 2 wh S = (2 · 4 · 6) + (2 · 4 · 3) + (2 · 6 · 3) Substitute. S = 48 + 24 + 36 Multiply. S = 108 The surface area of the prism is 108 in 2. Add. Course 2

Surface Area of Prisms, Cylinders, and 9 -4 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 r 2. Circumference r of cylinder (2 r) h Course 2

Surface Area of Prisms, Cylinders, and 9 -4 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 2

Surface Area of Prisms, Cylinders, and 9 -4 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 S = 2 r 2 + 2 rh 6 ft Use the formula. S (2 · 3. 14 · 62) + (2 · 3. 14 · 6 · 8. 3)Substitute. S 226. 08 + 312. 744 Multiply. Add. S 538. 824 Round. S 538. 8 The surface area of the cylinder is about 538. 8 ft 2. Course 2

Surface Area of Prisms, Cylinders, and 9 -4 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 S = 2 r 2 + 2 rh 9 ft Use the formula. S (2 · 3. 14 · 92) + (2 · 3. 14 · 9 · 20) Substitute. S 508. 68 + 1130. 4 Multiply. Add. S 1, 639. 08 Round. S 1, 639. 1 The surface area of the cylinder is about 1, 639. 1 ft 2. Course 2

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

Surface Area of Prisms, Cylinders, and 9 -4 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 the radius r squared. S= 4 r 2 Course 2

Surface Area of Prisms, Cylinders, and 9 -4 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 r 2 S 4 · 3. 14 · 82 S 803. 84 S 803. 8 Use the formula. Substitute. Multiply. Round. The surface area of the sphere is about 803. 8 m 2. Course 2

Surface Area of Prisms, Cylinders, and 9 -4 Spheres Try This: Example 3 Find the surface area of the sphere to the nearest tenth. Use 3. 14 for . 6 in. S = 4 r 2 S 4 · 3. 14 · 62 S 452. 16 S 452. 2 Use the formula. Substitute. Multiply. Round. The surface area of the sphere is about 452. 2 in 2. Course 2

Surface Area of Prisms, Cylinders, and 9 -4 Spheres Insert Lesson Title Here Lesson Quiz Find the surface area of each figure to the nearest tenth. 1. 2. 352. 0 ft 2 100. 5 ft 2 3. a sphere with radius 6 ft 452. 2 ft 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. 2, 317. 3 in 2 Course 2