87B Surface Area of Cylinders Essential Question Why are formulas important in math and science We will determine the lateral area and total surface area of cylinders I will solve problems involving the surface area of cylinders ID: 1002305
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1. Surface Area Lateral and Total Surface Area8.7B
2. Surface Area of CylindersEssential Question:Why are formulas important in math and science?We will… determine the lateral area and total surface area of cylinders.I will… solve problems involving the surface area of cylinders.
3. VocabularySurface Area- The total area of the surface of a 3D object. Lateral Area- The sum of the areas of the faces of a figure. (Not including the bases)
4. VocabularyTotal Surface Area- The sum of the areas of ALL the faces including the bases.
5. Lateral Surface area Formula: Cylinder S= 2rhS= lateral = 3.14r= radiush= height
6. Total Surface area Formula: Cylinder S= 2rh + 2S= lateral/Total surface area = 3.14r= radiush= height Lateral FormulaFinding the area of BOTH bases.
7. Lateral AreaPractice 1: 3 in7 inLateralBaseBaseIdentify the variables S= 2rhr= 3h=7 2. Plug in and SolveS= 2rhS= 2S= 131.88
8. Total Surface Area 3 in7 inBaseBase1. Formula S= 2rh + 22. Plug in and Solve22(3.14)()Area of BOTH bases=56.523. Add lateral & Area of both bases to get total surface area. S= 131.88 + 56.52 = 188.4 Lateral FormulaFinding the area of BOTH bases.
9. Total Surface Area:3. Add lateral & Area of both bases to get total surface area. S= 131.88 + 56.52 = 188.4 LateralArea of the Bases
10. Surface Area: Rectangular Prisms8.7B
11. We will use previous knowledge of surface area to make connections to the formulas for lateral and total surface area. I will solve for lateral and surface area of a rectangular prism.
12. What is the lateral area on a rectangular prism? Which are the bases?
13. Formulas:Lateral: S=PhP= perimeter of the base P=(2 x L) + (2 x w)h= heightTotal Surface area: S= Ph + 2BB=area of the base. B= L x w
14. Practice 1: Rectangular prism L= 12mW=6mh=7mFind the lateral area:S=PhS= (s+s+s+s)(h)2. Find the total surface area.S= Ph+2B
15. Total Surface area: S= Ph + 2B
16. Practice 2: Rectangular prismL=14 ftW= 7ftH=8ftFind the lateral area:S=PhS= (s+s+s+s)(h)2. Find the total surface area.S= Ph+2B
17. Practice 3: Rectangular prismL= 7 cmW= 3 cmH= 3 cmFind the lateral area:S=PhS= (s+s+s+s)(h)2. Find the total surface area.S= Ph+2B
18. Practice 4: Rectangular prismL=4.9 ftW= 3 ftH= 0.7Find the lateral area:S=PhS= (s+s+s+s)(h)2. Find the total surface area.S= Ph+2B
19. Practice 5: Rectangular prismL= 4 mW= 3 mH= 2 mFind the lateral area:S=PhS= (s+s+s+s)(h)2. Find the total surface area.S= Ph+2B
20. Surface Area: Triangular Prism 8.7B
21. Goal We will determine the lateral area and total surface area of triangular prisms.I will solve for lateral and surface area of a triangular prism.
22. Essential QuestionWhy are formulas important in math and science?
23. VocabularyBase of a triangular prism- the two congruent, opposite and parallel faces shaped like triangles. Height of the triangular prism- the length of a side that is perpendicular to both bases. Perimeter- the distance around a closed plane figure.
24. Triangular Prism .
25. FormulasS = Ph + 2B Total Surface AreaS=Ph Lateral Surface AreaP = Perimeter of the base/triangle P=(s+s+s) h= Height of the prismB = area of the base B=1/2bhb= base of the triangle
26. Triangle Lateral Surface Area S= Ph Solve for Lateral surface area. S= Ph S= (s+s+s)(h) S= (18+15+15)(13) S= 624 S = 624 ft squareh = 12 181513Dimensions Triangle:h= 12b= 18Rectangle:h=13w= 15
27. Triangle Total surface area S= Ph + 2BSolve for Total surface area. S= Ph + 2BS= (s+s+s)(h) + 2(1/2bh) S= (h = 12 181513Dimensions Triangle:h= b= Rectangle:h=w=
28. Triangle Lateral surface area P= Ph 1. Solve for lateral surface area.
29. Triangle Lateral surface area P= Ph + 2B1. Solve for lateral surface area.
30. Triangle Lateral surface area P= Ph 1. Solve for lateral surface area.
31. Triangle Lateral surface area P= Ph + 2B1. Solve for lateral surface area.
32. Triangle Lateral surface area P= Ph 1. Solve for lateral surface area.
33. Triangle Lateral surface area P= Ph + 2B 1. Solve for lateral surface area.