Presentation on theme: "Surface Area of Prisms & Cylinders"— Presentation transcript:
1Surface Area of Prisms & Cylinders Objectives:1) To find the surface area of a prism.2) To find the surface area of a cylinder.
2I. Surface Area of a Prism Prism – Is a polyhedron with exactly 2 , // faces, called bases.Name it by the shape of its bases.Bases are Rectangles:Lateral Faces – All faces that are not bases. (Sides)
3Right Prisms vs Oblique Prisms Right Prism – Edges are Altitudes.
4Lateral Area – The sum of the areas of the lateral faces (sides) Right Prisms - Lateral Faces are RectanglesA = l•wBase Area – The sum of the areas of the 2 basesRectangle: A = l•wTriangle: A = ½bhPolygon: A = ½bhTotal Surface Area = Lateral Area + Base Area
5Ex.1: Use the net to find the Surface Area of the rectangular Prism. Area of Bases: A = l•w2 different Lats: A = l•w45cm1233435152015203cm4cmSA = LA + Area of Bases= 70cm2 + 24cm2= 94cm2312
6Ex.2: Find the total surface area of the following triangular prism. 5cmLA = l•w (Area of Sides)(5 x 12) = 60cm2(6 x 12) = 72cm25cm12cm6cmArea of Triangle192cm2BA = ½bh= ½(6)(4)= 12cm2x 224cm253hSA = LA + BA= 192cm2 + 24cm2= 216cm2a2 + b2 = c2h = 52h = 46
7Ex.2: Find the total surface area of the following regular hexagonal prism. LA = l•w(10 x 12) = 120m2x 612m720m210BA = ½ap= ½(8.7)(60)= 260m2x 2520m210m30°aSA = LA + BA= 720m m2= 1240m25Tan 30 = 5/a.577 = 5/aa = 8.7
8II. Finding Surface Area of a Cylinder Has 2 , // basesBase → CircleC = 2πrA = πr2rheightrhr
9Net of a Cylinder: LA is just a Rectangle! LA = 2rh BA = r2 Area of a circleLA = 2rhBA = r2rCircumference of the circleSA = LA + 2BA
10Ex.4: SA of a right cylinder LA = 2rh= 2(6)(9)= 108ft2= 339.3ft26ftArea of BaseBA = r2= (6)2= 36ft29ftx 2SA = LA + BA= 339.3ft ft2= 565.5ft2= 72ft2= ft2
11What did I learn today?? Find the area of the lateral sides first!! Usually rectanglesBe careful, the rectangles are not always the same size.Second, find the area of the BaseRectangle, Triangle, Polygon, or a CircleThere are always 2 bases in prisms.Multiply by 2!