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

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Presentation on theme: "Surface Area of Prisms & Cylinders Objectives: 1) To find the surface area of a prism. 2) To find the surface area of a cylinder."— Presentation transcript:

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

2 I. 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)

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

4 Lateral Area – The sum of the areas of the lateral faces (sides) Right Prisms - Lateral Faces are Rectangles A = lw Base Area – The sum of the areas of the 2 bases Rectangle: A = lw Triangle: A = ½bh Polygon: A = ½bh Total Surface Area = Lateral Area + Base Area

5 Ex.1: Use the net to find the Surface Area of the rectangular Prism. 5cm 3cm 4cm 343 4 3 5 3 Area of Bases: A = lw 12 2 different Lats: A = lw 15201520 SA = LA + Area of Bases = 70cm 2 + 24cm 2 = 94cm 2

6 Ex.2: Find the total surface area of the following triangular prism. 6cm 5cm 12cm LA = lw (Area of Sides) (5 x 12) = 60cm 2 (6 x 12) = 72cm 2 BA = ½bh = ½(6)(4) = 12cm 2 x 2 x 2 24cm 2 a 2 + b 2 = c 2 h 2 + 3 2 = 5 2 h = 4 5 3 h 6 192cm 2 SA = LA + BA = 192cm 2 + 24cm 2 = 216cm 2 Area of Triangle

7 Ex.2: Find the total surface area of the following regular hexagonal prism. LA = lw (10 x 12) = 120m 2 x 6 BA = ½ap = ½(8.7)(60) = 260m 2 x 2 520m 2 720m 2 SA = LA + BA = 720m 2 + 520m 2 = 1240m 2 10m 12m 10 5 30° a Tan 30 = 5/a.577 = 5/a a = 8.7

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

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

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

11 What did I learn today??  Find the area of the lateral sides 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!


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