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CONFIDENTIAL 1 Geometry Surface Area of Prisms and Cylinders

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CONFIDENTIAL 2 Warm Up Draw the top, left, and right views of each object. Assume there are no hidden cubes. a. b.c.

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CONFIDENTIAL 3 Surface Area of Prisms and Cylinders Prisms and cylinders have 2 congruent parallel bases. A lateral face is not a base. The edges of the base are called base edges. A lateral edge is not an edges of a base. The lateral faces of a right prism are all rectangles. An oblique prism has at least one nonrectangular lateral face. Bases Base edges Bases lateral faces lateral edge Next Page:

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CONFIDENTIAL 4 An altitude of a prism or cylinder is a perpendicular segment joining the planes of the bases. The height of a three- dimensional figure is the length of an altitude. Surface area is the total area of all faces and curved surfaces of a three-dimensional figure. The lateral area of a prism is the sum of the areas of the lateral faces. altitude Next Page:

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CONFIDENTIAL 5 The net of a right prism can be drawn so that the lateral faces form a rectangle with the same height as the prism. The base of the rectangle is equal to the perimeter of the base of the prism. h a b c h a b c

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CONFIDENTIAL 6 Lateral Area and Surface Area of Right Prisms The lateral area of a right prism with base perimeter P and height h is L = ph. The surface area of a right prism with lateral area L and base area B is S = L + 2B, or S = Ph + 2B. The surface area of a cube with edge length s is S = 6s. 2 h s s s

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CONFIDENTIAL 7 The surface area of a right rectangular prism with length l, width w, and height h can be written as S = 2 lw + 2 wh + 2 lh.

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CONFIDENTIAL 8 Finding Lateral Areas and surface Areas of Prisms Find the lateral area and surface area of each right prism. Round to the nearest tenth, if necessary. 12 cm 6 cm 8 cm Next Page: A) The rectangular prism L = ph = (28)12 = 336 cm P = 2(8) + 2(6) = 28 cm S = Ph + 2 B = 336 + 2(6)(8) = 432 cm 2 2

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CONFIDENTIAL 9 B) The regular hexagonal prism 10 m 6 m 10 m 6 m L = Ph = 36(10) = 360 m S = Ph +2B =360 + 2(54 3 ) = 547.1 m 2 2 P = 6(6) = 36 m The base area is B = ½aP = 54 3 m.

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CONFIDENTIAL 10 Now you try! 1) Find the lateral area and surface area of a cube with edge length 8 cm. 1) lateral area = 256 cm 2 surface area = 384 cm 2

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CONFIDENTIAL 11 The lateral surface of a cylinder is the curved surface that connects the two bases. The axis of a cylinder is the segment with endpoints at the centers of the bases. The axis of a right cylinder is perpendicular to its bases. The axis of an oblique cylinder is not perpendicular to its bases. The altitude of a right cylinder is the same length as the axis. Bases Axis lateral surfaces oblique cylinder right cylinder

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CONFIDENTIAL 12 Lateral Area and Surface Area of Right Cylinders The lateral area of a right cylinder with radius r and height h is L = 2 rh. The surface area of a right cylinder with lateral area L and base area B is S = L + 2B, or S = 2 rh + 2 r. 2 r h r h 2 r

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CONFIDENTIAL 13 Finding Lateral Areas and Surface Areas of Right Cylinders A) Find the lateral area and surface area of each right cylinder. Give your answer in terms of. 2 m 5m Next Page:

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CONFIDENTIAL 14 B) A cylinder with a circumference of 10 cm and a height equal to 3 times the radius. Step 1 Use the circumference to find the radius. Step 2 Use the radius to find the lateral area and surface area. The height is 3 time the radius, or 15 cm.

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CONFIDENTIAL 15 Now you try! 2) Find the lateral area and surface area of a cylinder with a base area of 49 and a height that is 2 times the radius. 2) lateral area = 196∏ unit 2 surface area = 294∏ unit 2

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CONFIDENTIAL 16 Finding Surface Areas of composite Three- Dimensional Figures Find the surface area of the composite figure. Round to the nearest tenth. 4 ft 20 ft 16 ft 24 ft Next Page: The surface area of the right rectangular prism is S = Ph + 2B = 80(20) + 2(24)(16) = 2368 ft 2

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CONFIDENTIAL 17 A right cylinder is removed from the rectangular prism. The surface area of the composite figure is the sum of the areas of all surfaces on the exterior of the figure. 4 ft 20 ft 16 ft 24 ft

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CONFIDENTIAL 18 Now you try! 2 cm 3 cm 4 cm 9 cm 5 cm 3) Find the surface area of the composite figure. Round to the nearest tenth. 3) surface area = 239.7 cm 2

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CONFIDENTIAL 19 Exploring Effects of Changing dimensions The length, width, and height of the right rectangular prism are doubled. Describe the effect on the surface area. 3 in. 2 in. 6 in. Original dimensions: S = Ph + 2B = 16(3) + 2(6)(2) = 72 in 2 Length, width, and height doubled: S = Ph + 2B = 32(6) + 2(12)(4) = 288 in 2 Notice that 288 = 4(72). If the length, width, and height are doubled, the surface area is multiplied by 2, or 4. 2

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CONFIDENTIAL 20 Now you try! 14 cm 22 cm 4) The height and diameter of the cylinder are multiplied by ½. Describe the effect on the surface area. 4) prev. area = 1727 cm 2 new area = 431.75 cm 2. The surface area is decreased by 4 times.

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CONFIDENTIAL 21 Chemistry Application 1 cm 8 cm 3 cm 4 cm 2 cm If two pieces of ice have the same volume, the one with the greater surface area will melt faster because more of it is exposed to the air. One piece of ice shown is a rectangular prism, and the other is half a cylinder. Given that the volumes are approximately equal, which will melt faster? Next Page:

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CONFIDENTIAL 22 1 cm 8 cm 3 cm 4 cm 2 cm

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CONFIDENTIAL 23 Now you try! Use the information above to answer the following. 5) A piece of ice shaped like a 5 cm by 5 cm by 1 cm rectangular prism has approximately the same volume as the pieces in the previous slide. Compare the surface areas. Which will melt faster? 3 cm 4 cm 2 cm 5 cm 1 cm 5) Cube 2 will melt faster. CUBE 1 CUBE 2

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CONFIDENTIAL 24 Now some problems for you to practice !

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CONFIDENTIAL 25 Assessment 1) How many lateral faces does a pentagonal prism have? 1) 5 faces

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CONFIDENTIAL 26 2) Find the lateral area and surface area of each right prism. AB 3 ft 5 ft 7 ft 5 cm 2 cm 4 cm 3 cm 2a) lateral area = 72 ft 2 surface area = 142 ft 2 2b) lateral area = 24 cm 2 surface area = 36 cm 2

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CONFIDENTIAL 27 3) Find the lateral area and surface area of each right cylinder. Given your answers in terms of. 12 yd 15 yd 4 ft 3 ft 3a) lateral area = 24∏ ft 2 surface area = 42∏ ft 2 3b) lateral area = 180∏ yd 2 surface area = 292.5∏ yd 2

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CONFIDENTIAL 28 4) Find the surface area of each composite figure. Round to the nearest 4 ft 14 ft 8 ft 12 ft 6 ft 14 ft AB 4a) surface area = 833 ft 2 4b) surface area = 2855.0 ft 2

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CONFIDENTIAL 29 5) Describe the effect of each change on the surface area of the given figure. A) The dimensions are cut in half. B) The dimensions are multiplied by 2/3. 6 yd 8 yd 4 yd 8 yd 5a) surface area is decreased by 4 times. 5b) surface area is decreased by 4/9 times.

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CONFIDENTIAL 30 6) The greater the lateral area of a florescent light bulb, the more light the bulb produces. One cylindrical light bulb is 16 inches long with a 1- inch radius. Another cylindrical light bulb is 23 inches long with a ¾ inch radius. Which bulb will produce more light? 6) second bulb will produce more light.

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CONFIDENTIAL 31 Let’s review Surface Area of Prisms and Cylinders Prisms and cylinders have 2 congruent parallel bases. A lateral face is not a base. The edges of the base are called base edges. A lateral edge is not an edges of a base. The lateral faces of a right prism are all rectangles. An oblique prism has at least one nonrectangular lateral face. Bases Base edges Bases lateral faces lateral edge Next Page:

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CONFIDENTIAL 32 An altitude of a prism or cylinder is a perpendicular segment joining the planes of the bases. The height of a three-dimensional figure is the length of an altitude. Surface area is the total area of all faces and curved surfaces of a three-dimensional figure. The lateral area of a prism is the sum of the areas of the lateral faces. altitude Next Page:

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CONFIDENTIAL 33 The net of a right prism can be drawn so that the lateral faces form a rectangle with the same height as the prism. The base of the rectangle is equal to the perimeter of the base of the prism. h a b c h a b c

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CONFIDENTIAL 34 Lateral Area and Surface Area of Right Prisms The lateral area of a right prism with base perimeter P and height h is L = ph. The surface area of a right prism with lateral area L and base area B is S = L + 2B, or S = Ph + 2B. The surface area of a cube with edge length s is S = 6s. 2 h s s s

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CONFIDENTIAL 35 The surface area of a right rectangular prism with length l, width w, and height h can be written as S = 2 lw + 2 wh + 2 lh.

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CONFIDENTIAL 36 Finding Lateral Areas and surface Areas of Prisms Find the lateral area and surface area of each right prism. Round to the nearest tenth, if necessary. 12 cm 6 cm 8 cm Next Page: A) The rectangular prism L = ph = (28)12 = 336 cm P = 2(8) + 2(6) = 28 cm S = Ph + 2 B = 336 + 2(6)(8) = 432 cm 2 2

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CONFIDENTIAL 37 B) The regular hexagonal prism 10 m 6 m 10 m 6 m L = Ph = 36(10) = 360 m S = Ph +2B =360 + 2(54 3 ) = 547.1 m 2 2 P = 6(6) = 36 m The base area is B = ½aP = 54 3 m.

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CONFIDENTIAL 38 The lateral surface of a cylinder is the curved surface that connects the two bases. The axis of a cylinder is the segment with endpoints at the centers of the bases. The axis of a right cylinder is perpendicular to its bases. The axis of an oblique cylinder is not perpendicular to its bases. The altitude of a right cylinder is the same length as the axis. Bases Axis lateral surfaces oblique cylinder right cylinder

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CONFIDENTIAL 39 Lateral Area and Surface Area of Right Cylinders The lateral area of a right cylinder with radius r and height h is L = 2 rh. The surface area of a right cylinder with lateral area L and base area B is S = L + 2B, or S = 2 rh + 2 r. 2 r h r h 2 r

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CONFIDENTIAL 40 Finding Lateral Areas and Surface Areas of Right Cylinders A) Find the lateral area and surface area of each right cylinder. Give your answer in terms of. 2 m 5m Next Page:

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CONFIDENTIAL 41 B) A cylinder with a circumference of 10 cm and a height equal to 3 times the radius. Step 1 Use the circumference to find the radius. Step 2 Use the radius to find the lateral area and surface area. The height is 3 time the radius, or 15 cm.

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CONFIDENTIAL 42 Finding Surface Areas of composite Three- Dimensional Figures Find the surface area of the composite figure. Round to the nearest tenth. 4 ft 20 ft 16 ft 24 ft Next Page: The surface area of the right rectangular prism is S = Ph + 2B = 80(20) + 2(24)(16) = 2368 ft 2

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CONFIDENTIAL 43 A right cylinder is removed from the rectangular prism. The surface area of the composite figure is the sum of the areas of all surfaces on the exterior of the figure. 4 ft 20 ft 16 ft 24 ft

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CONFIDENTIAL 44 Exploring Effects of Changing dimensions The length, width, and height of the right rectangular prism are doubled. Describe the effect on the surface area. 3 in. 2 in. 6 in. Original dimensions: S = Ph + 2B = 16(3) + 2(6)(2) = 72 in 2 Length, width, and height doubled: S = Ph + 2B = 32(6) + 2(12)(4) = 288 in 2 Notice that 288 = 4(72). If the length, width, and height are doubled, the surface area is multiplied by 2, or 4. 2

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CONFIDENTIAL 45 Chemistry Application 1 cm 8 cm 3 cm 4 cm 2 cm If two pieces of ice have the same volume, the one with the greater surface area will melt faster because more of it is exposed to the air. One piece of ice shown is a rectangular prism, and the other is half a cylinder. Given that the volumes are approximately equal, which will melt faster? Next Page:

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CONFIDENTIAL 46 1 cm 8 cm 3 cm 4 cm 2 cm

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CONFIDENTIAL 47 You did a great job today!

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