Presentation on theme: "3.2a: Surface Area of Prisms and Cylinders"— Presentation transcript:
1 3.2a: Surface Area of Prisms and Cylinders PrimaryM(G&M)–10–6 Solves problems involving perimeter, circumference, or area of two dimensional figures (including composite figures) or surface area or volume of threeSecondaryM(G&M)–10–2 Makes and defends conjectures, constructs geometric arguments, uses geometric properties, or uses theorems to solve problems involving angles, lines, polygons, circles, or right triangle ratios (sine, cosine, tangent) within mathematics or across disciplines or contexts (e.g., Pythagorean Theorem, Triangle Inequality Theorem)
2 Prism: a 3-D solid with 1) 2 bases – which are parallel and congruent 3-D figures- Solid figures. When the sides are polygons, its called a polyhedron.Prism: a 3-D solid with 1) 2 bases – which are parallel and congruent2) lateral faces that are parallelograms* names by the shape of their basesBaseLateral EdgeAltitude (height)- Distance between thebasesBase (parallel & Congruent)Lateral Face – parallel sides not the base
3 Areas of the SolidsLateral Area (LA) – the sum of the areas of the lateral faces only.Does not include the area of the bases.Surface Area (SA) – the sum of the areas of ALL the faces.Lateral area + area of the bases
4 Lateral Area of a Right Prism P = Perimeter of the baseh= height between the bases (altitude)Surface Area of a Right PrismB = Area of one Base
5 Ex: Find the lateral & surface areas of the triangular prism. LA = PhP = 6*3 = 18LA = 18*10LA = 180 in2S = 2B + PhS = 2(15.59) + 180S =S = in26 in.60o10 in.
11 A right cylinder has a surface area of 400 square mm. ExampleA right cylinder has a surface area of 400 square mm.Find the height of the cylinderif the diameter of the base of the cylinder is 10 mm.
12 example2If the side of a cube is doubled, what happens to the surface area ?
13 The Lateral Area of a right rectangular prism is 784 square cm. ChallengeThe Lateral Area of a right rectangular prism is 784 square cm.Its length is three times its width.Its height is twice its width.Find the surface area.
14 Ex. 1 – Released Item from 2007 NECAP A square with a side length of 8.0 cm is rolled up, without overlap, to form the lateral surface of a cylinder.What is the radius of the cylinder to the nearest tenth of a centimeter?Ex 2. Find the Surface Area13 in4 in12 in5 in