Surface Area of Prisms and Cylinders Key
Surface Area of Prisms and Cylinders Key
Surface Area of Prisms and Cylinders Key
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<strong>Surface</strong> <strong>Area</strong> <strong>of</strong> <strong>Prisms</strong> <strong>and</strong> <strong>Cylinders</strong> KEYGeometryHS MathematicsUnit: 10 Lesson: 01Besides using nets, the surface area <strong>of</strong> right prisms, cylinders, pyramids, <strong>and</strong> cones can becalculated using formulas. Nets can also be used to verify calculations.STAAR Geometry Reference MaterialsExample:1. Find the lateral <strong>and</strong> total surface area <strong>of</strong> a prism with height <strong>of</strong> 15 inches containing righttriangular bases with legs 5 inches <strong>and</strong> 12 inches in square inches <strong>and</strong> in square centimeters.(1 inch = 2.54 centimeters)LA = 450 square inchesSA = 510 square inchesLA ≈ 2903.22 square centimetersSA ≈ 3290.32 square centimeters©2012, TESCCC 10/26/12 page 1 <strong>of</strong> 3
<strong>Surface</strong> <strong>Area</strong> <strong>of</strong> <strong>Prisms</strong> <strong>and</strong> <strong>Cylinders</strong> KEYGeometryHS MathematicsUnit: 10 Lesson: 01Practice Problems:1. Anna’s room is in the shape <strong>of</strong> a regular hexagonal prism with the width <strong>of</strong> each wall being 16feet along the baseboard. The height <strong>of</strong> the room is 10 feet.a. Anna wants to put new wallpaper up on all her walls. What is the minimum amount <strong>of</strong>square feet <strong>of</strong> wallpaper will she need to cover the walls?LA = 960 square feetb. The label on the wallpaper she will be using says that each roll covers 125 square feet.How many rolls will Anna need to purchase?7.68 rolls; therefore, she must purchase 8 rolls.c. If Anna wants to paint the ceiling gray, how many square feet will she need to cover?665 square feet2. A cylindrical grain silo is being built for Mr. Greenjeans. The silo is 13 meters tall with adiameter <strong>of</strong> 6 meters. If the entire silo is being fabricated from sheet metal, how many squaremeters <strong>of</strong> sheet metal will be needed to complete the silo? How many square feet <strong>of</strong> sheetmetal will be needed to complete the silo? (3.28 feet = 1 meter)SA ≈ 301.6 square metersSA ≈ 3244.7 square feet©2012, TESCCC 10/26/12 page 2 <strong>of</strong> 3
<strong>Surface</strong> <strong>Area</strong> <strong>of</strong> <strong>Prisms</strong> <strong>and</strong> <strong>Cylinders</strong> KEYGeometryHS MathematicsUnit: 10 Lesson: 013. For each prism or cylinderi. Name the figure.ii. Find the approximate lateral surface area.iii. Find the approximate total surface area.a. b.Right Regular PentagonalPrismLA = 2034.3 square feetSA = 2499.3 square feetRight Circular CylinderLA ≈ 11,963.2 square mmSA ≈ 19,226.5 square mm35 ft56 mm8 ft34 mm4. A cardboard tube from a roll <strong>of</strong> Christmas wrapping paper has a diameter <strong>of</strong> 6.75 centimeters<strong>and</strong> a height <strong>of</strong> 1.2 meters. What is the minimum number <strong>of</strong> square meters <strong>of</strong> cardboardnecessary to make 2500 tubes for holding Christmas wrapping paper? How many squareinches <strong>of</strong> cardboard is need to make one wrapping paper tube? (1 inch = 2.54 centimeters)Approximately 636.2 square meters <strong>of</strong> cardboard for 2500 tubesApproximately 394.43 square inches <strong>of</strong> cardboard for one tube5. Carl’s Camping Supplies makes a one person pup tent from waterpro<strong>of</strong> canvas tarp. Each tentis in the shape <strong>of</strong> a right prism whose bases are equilateral triangles with edges <strong>of</strong> 4 feet. Whatis the minimum number <strong>of</strong> square feet <strong>of</strong> material necessary to produce one 7-foot long tent,including bottom <strong>and</strong> end flaps? How many square meters <strong>of</strong> material would be necessary tocomplete the same 7-foot tent? (3.28 feet = 1 meter)Each tent will require approximately 98 square feet <strong>of</strong> canvas tarp.Each tent will require approximately 9 square meters <strong>of</strong> canvas tarp.©2012, TESCCC 10/26/12 page 3 <strong>of</strong> 3
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