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Surface Area and Volume of Prisms & Cylinders Surface Area and Volume 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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I. Surface Area of a Prism Prism – Is a polyhedron with exactly 2 congruent, parallel faces, called bases. Name it by the shape of its bases. Bases are Rectangles: Lateral Faces – All faces that are not bases. (Sides)

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Right Prisms vs Oblique Prisms Right Prism – Lateral faces are rectangles. Oblique Prism – Lateral faces are parallelograms

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Total Surface Area = Lateral Area + 2 Base Area Lateral Area – If the base is a regular polygon all 4 rectangles will be congruent If the base is a non regular polygon you should look at individual rectangles and calculate their areas with A = lw

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Base Area – Rectangle: A = lw Triangle: A = ½bh Total Surface Area = Lateral Area + 2 Base Area

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Ex.1: Find the Surface Area of the rectangular Prism. 5cm 3cm 4cm Area of Bases: A = lw = 43 = 12 cm 2 Lateral Area Left and right rectangles are congruent A = lw= 35 = 15 cm 2 Front and back rectangles are congruent A = lw= 45 = 20 cm 2 Total = 15+15+20+20 =70 cm 2 SA = LA + BA = 70cm 2 + 24cm 2 = 94cm 2

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

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Ex.2: Find the total surface area of the following regular hexagonal prism. LA = lw (10 x 12) = 120m 2 x 6 BA = ½ans = ½(8.7)(6)(10) = 260m 2 x 2 520m 2 720m 2 SA = LA + BA = 720m 2 + 520m 2 = 1240m 2 10m 12m a 8.7

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

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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

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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

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