Surface Area of Prisms & Cylinders

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12.2 Surface Area of Prisms & Cylinders

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Surface Area of Prisms & Cylinders

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Presentation transcript:

Surface Area of Prisms & Cylinders Objectives: 1) To find the surface area of a prism. 2) To find the surface area of a cylinder. Ms. Olifer

I. Surface Area of a Prism Prism – Is a polyhedron w/ 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)

Right Prisms vs Oblique Prisms Right Prism – Edges are Altitudes.

Lateral Area – The sum of the areas of the lateral faces (sides) LA = Ph Base Area – The sum of the areas of the 2 bases Rectangle: A = l•w Triangle: A = ½bh Total Surface Area = Lateral Area + 2Base Area

Ex.1: Find the Surface Area of the rectangular Prism. Area of Bases: A = l•w 5cm 3cm 4cm SA = LA + BA = 70cm2 + 24cm2 = 94cm2

Ex. 2: Find the total surface area of the following triangular prism Ex.2: Find the total surface area of the following triangular prism. The base is an isosceles triangle. 5cm 5cm 12cm LA = Ph 6cm 192cm2 BA = ½bh = ½(6)(4) = 12cm2 x 2 24cm2 5 h SA = LA + BA = 192cm2 + 24cm2 = 216cm2 a2 + b2 = c2 h2 + 32 = 52 h = 4 3 6

II. Finding Surface Area of a Cylinder Has 2 , // bases Base → Circle C = 2πr A = πr2 r height r h r

Net of a Cylinder: LA is just a Rectangle! LA = 2rh BA = r2 Area of a circle LA = 2rh BA = r2 r Circumference of the circle SA = LA + 2BA

Ex.4: SA of a right cylinder LA = 2rh = 2(6)(9) = 108ft2 = 339.3ft2 6ft Area of Base BA = r2 = (6)2 = 36ft2 9ft x 2 SA = LA + BA = 339.3ft2 + 226.2ft2 = 565.5ft2 = 72ft2 = 226.2 ft2

What did I learn today?? Find the area of the lateral faces first!! Usually rectangles Be careful, the rectangles are not always the same size. Second, find the area of the Base Rectangle, Triangle, Polygon, or a Circle There are always 2 bases in prisms. Multiply by 2!