Lesson 6 Reteach. Surface Area of Prisms. Example. Exercises. 232 in^ tt^^ Find the surface area of the rectangular prism.

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1 Lesson 6 Reteach Surface Area of Prisms T h e s u m of the areas of all the surfaces, or faces, of a three-dimensional shape is the surface area. T h e surface area of a rectangular prism with length f, w/idth w, and height h is the s u m of the areas of its faces. = 2 w + 2eh + 2wh Find the surface area of the rectangular prism. Faces Area J top and bottom front and back two sides 2 (4. 3) = 24 2 (4. 2) = 16 2 (2. 3) =^ 12 back side bottom side sum of the areas 24 -I = 52 front Alternatively, replace { with 4, w with 3, and h with 2 in the formula for surface area. ^ 2iw + 2f.h + 2wh top = 2 (4 3) -f- 2 (4. 2) 2 (3 2) e s I = = 52 So, the surface area of the rectangnlar prism is 52 square meters. Find the surface area of each prism S 2 in. 232 in^ \Z 4,9 ft " / S f t 0.7 ft 9 mm tt^^ Course 2 Chapter 8 Measure Figures 131

2 Lesson 4 Reteach Surface Area of Cylinders T h e surface area of a cylinder with height h and radius r is the s u m of the area of the curved surface and the area of the circular bases. = 2wh + 2irr2 Find the total surface area of the cylinder. Round to the nearest tenth. 8 m = 2'Krh + 2-iTr'' Surface area of a cylinder = 2'jr(6)(8) + 2TT(6)^ Replace r with 6 and h with 8. ^ Simplify. The surface area of the cylinder is about square meters. Find the total surface area of each cylinder. Round to the nearest tenth. J, yd= In. 1,288.1 in^ 3. 5 cm 20 cm D 353.^ m m2 Course 3 Chapter 8 Volume and Surface Area 123

3 Lesson 7 Reteach Surface Area of Pyramids T h e total surface area of a regular pyramid is the lateral area L.A. plus the area of the base. = e + LA. or =B + ^Pf. Slant height Area of base B Perimeter of base P 1 Find the total surface area of the pyramid. 6 in. = B+-^P Surface area of a pyramid = (28 6) P = 4(7) or 28, = 6, fi = 7 7 or 49 = 133 Simplify. 7 in. The surface area of the pj-tamid is 133 squai-e inches. 2 Find the total surface area of the pyramid. =B + ^Pi' Surface area of a pyramid area of base 15.6 m2 = <18 5) = 60.6 P = 3(6) or 18. = 5, B = 15.6 Simplify. The surface area of the pyramid is 60.6 square meters. Find the total surface area of each pyramid. Round to the nearest tenth cm area of base 6.9 cm^ 16 ft^^ Coune 2 Chapter 8 Measure Figures 48.9 cm^ 133

4 Lesson 5 Reteach Surface Area of Cones T h e lateral area L.A. of a cone is TT times the radius times the slant height, or L.A. = irrl T h e total surface area of a cone with slant height I and radius r is the lateral area plus the area of the base, or = LA. + TTi^ or - nrl + m^. Find the lateral and total surface areas of the cone. Round to the nearest tenth. Lateral Surface Area L. A. = -KH L A. - TT-S'S r=:3, f = 5 L. A. «47.1 Total Surface Area = L. A. + -rrr^ ~ 75.4 The lateral and total surface areas of the cone are about 47.1 and 75.4 square centimeters. Find the lateral and total surface areas of each cone. Round to the nearest tenth. 1. A\ cm^; cm^ W ft 17 m' 7.3 ft ft^; ft^ m^'; Course 3 Chapter 8 Volume and Surface Area 125

5 Lesson 6 Reteach Changes in Dimensions A scale factor is how much larger or smaller one solid is than another. Similar solids have the same shape and their corresponding linear measures are proportional. For similar solids A and S: surface area of S (surface area of A) x (scale factor)^ 1 The surface area of a rectangular prism is 144 square centimeters. Find the surface area of a similar prism that is larger by a scale factor of P- Multiply by the square of the scale factor. = Square 4. = 2,304 c m ^ Simplify. For similar solids -4 and B: Volume of S = (volume of A) x (scale factor)* 2 The volume of a rectangular prism is 120 cubic feet. Find the volume of a similar prism that is larger by a scale factor of 2. V 120 2^ Multiply by the cube of the scale factor. F = Cube 2. V = 960 ft'^ Simplify 1. The surface area o f a rectangular prism is 1,150 square inches. Find the surface area of a similar prism that is larger by a scale factor of 2. 4,600 in^ 2. The surface area of a pyramid is 38 square feet. What is the surface area of a similar pyramid that is smaller by a scale factor of-5-? Round to the nearest tenth. 4.2 ft^ J 3. The volume o f a triangular prism is 5 cubic meters. Find the volume o f a similar prism that is larger by a scale factor o f The volume o f a cylinder is 416 cubic inches. What is the volume o f a similar cylinder that is smaller by a scale factor of -i? 52 in^ Course 3 Chapter 8 Volume and Surface Area 127