5 Prism: A solid object that has two identical ends (bases) and all flat sides Discuss the idea of bases also refer to the previous slide and discuss how in a rectangular prism you can technically use any pare of parallel sides as the bases. Typically people view the base as the pair that can be considered the top and the bottom of the rectangular prism.Triangular Prism
8 Rectangular Prism Base 2 Bottom Back Top Base 1 Front Top Back Side 2 Height (H)BottomIn this slide you begin the development of what is surface area. The shape will be broken up identify what shapes make up the outer surface of this shape. Also discuss what the shape is. It will break up into its rectangular parts as it does discuss the opposite sides and their relationship.Base (B)Length (L)
10 Surface Area - the total area of all the faces (surfaces) of an object. To find the surface area of an object we can add up the areas of the separate faces. Note: some faces have the same size and shapeSurface Area of this prism:Add the areas of the two brown sides (A) to the two green sides (D) and to the two red sides (C).CDAwhlThis is a rectangular prism. The l, w and h have different values.
11 Surface AreaFind the surface area of the rectangular prismWe should use a table to tabulate the various areas.FaceAreaNumber of SidesTotal AreaA12cm2224cm2D15cm230cm2C20cm240cm2TOTAL694cm2CDA3 cm5 cm4 cmArea of rectangle = l x w
12 Volume5 cmBB2 cmBhhhThe number of cubic units needed to fill the space occupied by a solid.3 cmVOLUME OF A PRISMThe volume V of a prism is the area of its base B times its height h.V = BhNote – the capital letter stands for the AREA of the BASE not the linear measurement.Volume = Base area x height= (l x w) x height= (3 cm x 2 cm) x height= 6 cm2 x 5 cm= 30 cm3Discuss why this is a unit cube and the volume vormulaArea of rectangle = l x w
13 Prism Volume Example V = Bh = (4ft x 3ft)h = (12 ft2)h Find area of the base 1st= (4ft x 3ft)h= (12 ft2)hMultiply it by the height= (12 ft2) x 8 ft= 96 ft33 ftB4 ft8 ftArea of rectangle = l x w
14 What is the surface area and volume of the prism? SA rectangle = l x wSA (rect1) = 12 cm x 10 cm= 120 cm2 x 2 = 240 cm2SA (rect2) = 12 cm2 x 22 cm= 264 cm2 x 2 = 528 cm2SA (rect3) = 10 cm x 22 cm2= 220 cm2 x 2 = 440 cm2Total SA = SA (rect1) + SA (rect2) + SA(rect3)= 240 cm cm cm2= cm210 cmB12 cm22 cmV = Bh= (12 cm x 10 cm) x h= (120 cm2) x 22 cm= 2640 cm3Note Units
16 Surface Area of a triangular prism 2 area of same triangle + 2 areas of 3 rectangles, which 2 are the same15ftArea Triangle 1 & 2 = 𝑏ℎ 2= 12 𝑓𝑡 𝑥 15 𝑓𝑡 2= 180 ft2 2= 90 ft2Area Rect. 1 = l x w= 12 ft x 25 ft= 300 ft2Area Rect. 2 & 3 = 25 ft x 20 ft= 500 ft2SA=triangle1 + triangle2 + rectangle1 + rectangle2 + rectangle3SA=+ 300+ 500+ 500SA = 1480 ft2
17 Volume of a triangular prism Area Triangles = 𝒃𝒉 𝟐= 𝟏𝟐 𝒙 𝟏𝟓 𝟐= 𝟏𝟖𝟎 𝟐= 90 ft2V= BhFind area of the base= (90 ft2)hMultiply it by the height= (90 ft2) x 25 ft= 2250 ft315ft
19 Cylinder Bases Cylinder Discuss how prisms and cylinders have similar ways of looking at the base they are congruent parrallel and there are 2.Cylinder
20 SA of a CylinderFormula for Area of CircleA= r2= 3.14 x 32= 3.14 x 9= 28.26But there are 2 of them so28.26 x 2 = units squaredFind the circumference to determine the length of the rectangleC = x d= 3.14 x 6 (radius doubled)= 18.84Now use that as your base.A = b x h= x 6 (the height given)= units squaredNow add the area of the circles and the area of the rectangle together.= units squaredThe total Surface Area!
21 Volume of a Cylinder = (28.26)h = 169.56 unit3 V= Bh Formula for Area of CircleA= r2= 3.14 x 32= 3.14 x 9= unit2V= BhFind area of the base= (28.26)hMultiply it by the height= (28.26) x 6= unit3
22 Calculate the SA and Volume of the cylinder Be sure you know the difference between a radius and a diameter!Formula for Area of CircleA= r2= 3.14 x 52= 3.14 x 25= 78.54But there are 2 of them so78.54 x 2 = units squaredV = BhC = x d= x 10 (radius doubled)= 31.15Now use that as your base.A = b x h= x 4.2 (the height given)= units squaredThe radius of the cylinder is 5 m, and the height is 4.2 m; therefore B = A = r = 3.14 · 52 = m2V = BhV = · 4.2V = m3SA = = m2