10-3 Surface Area of Prisms and Cylinders

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Surface Area of Prisms & Cylinders Geometry Mr. Westlove Summer 2009.

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10-3 Surface Area of Prisms and Cylinders 5/22/17 PRISM: a polyhedron with exactly two congruent parallel faces, called BASES. Other faces are LATERAL FACES. ALTITUDE: perpendicular segment that joins the planes of the bases HEIGHT (h): of the prism is the length of an altitude

LATERAL EDGES BASES BASES LATERAL FACES Pentagonal Prism Triangular Prism

A prism may either be right or oblique. RIGHT PRISM OBLIQUE PRISM LATERAL AREA: of a prism is the sum of the area of the lateral faces SURFACE AREA: the total sum of all the sides (the lateral area and the area of the two bases). Just add the areas of ALL sides

Ex: Find the lateral area and the surface area of the prism. (Not the bases) Ex: Find the lateral area and the surface area of the prism. First find the third side of the triangle 3 4 3-4-5 Triple or use the Pyth. Theorem 5 6 b) Three lateral faces: all rectangles A = lw 3 x 6 = 18 4 x 6 = 24 5 x 6 = 30 72 cm2 is the lateral area c) Easier method: Lateral Area = Perimeter•Height (3 + 4 + 5)•6 = 72 d) SA = 2 • ½ • 3(4) + 72 = 84 cm2

CYLINDER: has 2 congruent parallel bases that are circles The ALTITUDE of a cylinder is a perpendicular segment that joins the planes of the bases. The HEIGHT h of a cylinder is the length of an altitude. Bases h h RIGHT CYLINDER OBLIQUE CYLINDER

Lateral area is the area of the unrolled rectangle Lateral area is the area of the unrolled rectangle. Surface area is the sum of the rectangle and the two areas of the circular bases. A = r2 h Lateral area Surface area 2 r (add area of all 3 parts) LATERAL AND SURFACE AREAS L.A. = 2 rh or L.A. = dh r S.A. = 2 rh + 2 r2 h

Ex: The radius of the base of a cylinder is 4”, and the height is 6” Ex: The radius of the base of a cylinder is 4”, and the height is 6”. Find the surface area in terms of . r = 4 and h = 6 S.A. = 2 rh + 2 r2 = 2 (4)(6) + 2 (4)2 = 48 + 32 = 80 in2 1) Find the surface area of a cylinder with height 12 cm and radius 10 cm in terms of SA = 2 (10)(12) + 2 (10)2 = 240 + 200 = 440

LA = P•H (with top/bottom bases) = 22•4 = 88 Bases = (3)(8)•2 = 48 Find the surface area 1) 8 2) 4 4 cm 3 cm 3 8 cm 3) 3 ft 12 ft LA = P•H = 12•8 = 96 SA = 108 SA = 136 cm2 Bases = ½(3)(4)•2 = 12 SA = 2πrh + 2πr2 = 2π(3)(12) + 2π(3)2 SA = 72π + 18π = 90π ft2 Assignment: Page 531 #1 – 6, 9 – 13, 22, 23, 27, 28