Surface Area of Prisms & Cylinders Objectives: 1) To find the surface area of a prism. 2) To find the surface area of a cylinder. 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) Right Prisms vs Oblique Prisms Right Prism Edges are Altitudes.
Oblique Prism 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 = bh Polygon: A = bh Total Surface Area = Lateral Area + Base Area Ex.1: Use the net to find the Surface Area of the rectangular Prism. Area of Bases: A = lw 2 different Lats: A = lw 4
5cm 3cm 4cm 3 4 3 15 20 15 SA = LA + Area of Bases = 70cm2 + 24cm2 = 94cm2
12 3 20 5 12 3 Ex.2: Find the total surface area of the following triangular prism. 5cm LA = lw (Area of Sides) (5 x 12) = 60cm2 5cm (5 x 12) = 60cm2
12cm (6 x 12) = 72cm2 Area of Triangle 6cm 192cm2 BA = bh = (6)(4) = 12cm 2 x2 24cm2 a2 + b2 = c2 h2 + 32 = 52 h=4
h 5 SA = LA + BA = 192cm2 + 24cm2 6 3 = 216cm2 Ex.2: Find the total surface area of the following regular hexagonal prism. LA = lw (10 x 12) = 120m2 x 6 12m 720m2
BA = ap = (8.7)(60) = 260m 2 x2 520m2 10 30 a 5 10m SA = LA + BA Tan 30 = 5/a = 720m2 + 520m2
.577 = 5/a = 1240m2 a = 8.7 II. Finding Surface Area of a Cylinder Cylinder Has 2 , // bases Base Circle r C = 2rr A = rr2 height r h
r Net of a Cylinder: LA is just a Rectangle! LA = 2rh Area of a circle BA = r2 r Circumference of the circle SA = LA + 2BA Ex.4: SA of a right cylinder LA = 2rh 6ft
9ft = 2(6)(9) Area of Base = 108ft2 BA = r2 = 339.3ft2 = (6)2 = 36ft2 x2 SA = LA + BA = 72ft2 = 339.3ft2 + 226.2ft2
= 226.2 ft2 = 565.5ft2 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!
Center of gravity and Centroids MET 2214 Center of gravity and Centroids MET 2214 CENTER OF GRAVITY, CENTER OF MASS AND CENTROID FOR A BODY Objective : a) Understand the concepts of center of gravity, center of mass, and centroid.
CHAPTER 3:PHYSICAL EVIDENCE. Learning Objectives: List the common types of physical evidence found at crime scenes. Explain the difference between the identification and comparison of physical evidence. Define individual and class characteristics. Give examples of physical evidence possessing these characteristics.
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