Lesson 6 Reteach. Perimeter of the base = 14. S. A. = area of the 2 bases + lateral area = = 52 m^.
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1 Lesson 6 Reteach Surface Area of Prisms The sum of the areas of all the surfaces, or faces, of a three-dimensional shape is the surface area. Find the surface area of the rectangular prism. The area of one base is 4»3 = 12 m^. There are 2 bases so the total area of the bases = 24 m^. The Lateral Area is a big, long rectangle where the height is 2 m (the height of the prism) and the length of the long width is the perimeter of the base because it goes aroimd the entire base. Perimeter of the base is = 14 m. Lateral Area = 14«2 = 28 m^. 4 J 4 m Perimeter of the base = 14 S. A. = area of the 2 bases + lateral area = = 52 m^. Find the surface area of each prism cm 2 in. 3 cm 8 in. 3. Z 4.9 ft 3ft 0.7 ft 4. 8 mm 15 mm 17 mm mm Course 2 Chapter 8 Measure Figures
2 Lesson 4 Reteach Surface Area of Cylinders The surface area S.A. of a cylinder with height h and radius r is the sum of the area of the curved side, which is just a big rectangle Gust as wrapping paper or paper towels are rectangles when you unroll them), and the area of the two circular bases. The rectangle's base is the circle's circumference and its height is the height of the cylinder. S.A. = Area of the 2 circular bases + Lateral Area rectangle S.A. = 27Tr2 + 2rrrf) Find the total surface area of the cylinder. Round to the nearest tenth. m.- 6nr 8m S.A. = itcrh + litp- Surtece area of a cylinder SA. = 2K(6)(8) + 2<6y Replace rwith 6 and /? with 8. S.A. ~ The surface area of the cylinder is about square meters. Find the total surface area of each cylinder. Round to the nearest tenth in. 3, 5 cm 20 cm 4. 10m 3 m Course 3 Chapter 8 Volume and Surface Area 123
3 baseb Perimeter of base P 1 Find the total snrface area of the pyramid.. 6 in. 1 SA. = 49+ 1(2% ' 6) Surface area of a pyramid P = 4(7) or 28, ^= 6. e = 7 7 or 49 7 in. SA Simplify The surface area of the pyramid is 133 square inches. 2 Find the total surface area of the pyramid. S.A. = B + area of base SA. = m2 5.^. = i(18«5) Surface area of a pyramid P= 3(6) or 18,/= 5,3= 15.6 The surface area of the pyramid is 60.6 square meters. Find the total surfoce area of each pyramid. Round to the nearest tenth cm area of base 6.9 cm^ Course 2 Chapter 8 Measure Figures ft 3ft 8 mm 15 mm 9 mm Course 2 Chapter 8 Measure Figures 131
4 Lesson 5 Reteach Surface Area of Cones The lateral area L.A. of a cone is n times the radius times the slant height, or L.A. = nrt. The total surface area of a cone with slant height ^and radius r is the lateral area plus the area of the base, or S.A. = LA. + nr^ or S.A. = m ( + nr^. Find the lateral and total surface areas of the cone. Round to the nearest tenth. Lateral Surface Area LA. = nrt L.A. = n' I) ' 5 r=3,f=5 L.A. «47.1 Total Surface Area S.A.= L.A. + nr^ 5. A =47.1+ TT.32 S.A. «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. 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 6: 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 4. S.A. = 144 4^^ S.^.^ Square 4. SA. =^ 2,304 cm^ Multiply by the square of the scale factor. For similar solids A 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. F = 120 2^ Multiply by the cube of the scale fector. F= Cube 2. F=960ft^ 1. The surface area of a rectangular prism is 1,150 square inches. Find the surface area of a similar prism that is larger by a scale factor of 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 ^? Round to the nearest tenth. 3. The volume of a triangular prism is 5 cubic meters. Find the volume of a similar prism that is larger by a scale factor of3. 4. The volume of a cylinder is 416 cubic inches. What is the volume of a similar cylinder that is smaller by a scale factor of i? Course 3 Chapter 8 Volume and Surface Area 127
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