March 14, 2011March 14, 20111) Write your homework in your agenda: 1) Write your homework in your agenda: Homework and Practice wkbk Homework and Practice wkbk Lesson 10-9 Surface AreaLesson 10-9 Surface Area

SHOW ALL YOUR WORK!!SHOW ALL YOUR WORK!!2) Turn in your Surface Area Performance 2) Turn in your Surface Area Performance

Task. Put your name on it.Task. Put your name on it.3) Set up for Cornell Notes and then open 3) Set up for Cornell Notes and then open

your dictionary to the Solid Figures section.your dictionary to the Solid Figures section.

Surface AreaSurface AreaWhat am I Learning Today?What am I Learning Today?

How will I show that I learned it?How will I show that I learned it?Derive a formula for the surface area of

prisms and cylinders using 2D figures, manipulatives and nets

Compute surface area using formulasSolve application problems involving

surface area

VocabularyVocabularySurface area: The Surface area: The sumsum of the area of of the area of

the faces of a solid figure the faces of a solid figure

Top

Side

Front

l

h

w Top

Bottom

Front

Back

Right SideLeft Side

Formula for Surface Area derived from the nets.

Each surface is a rectangle.Each rectangle has a congruent counterpart.

Find the area of each surface.A = lw

Then multiply each area by 2.A = 2(lw)A = 2(wh)A = 2(lh)

Find the Total Surface Area by adding these areas together.SA = 2(lw) + 2(wh) + 2(lh)

h

h

l

h

w

w

lWhere do the formulas come from?Where do the formulas come from?

Where do the formulas come from?Where do the formulas come from?

Prism Surface Area FormulaPrism Surface Area FormulaTop Length x Width

Bottom Length x WidthFront Height x LengthBack Height x LengthLeft Height x Width

Right Height x WidthTotalTotal lw + lw + hl + hl + hw + hw

Surface Surface Area Area

FormulaFormula2lw + 2hl + 2hw

Where do the formulas come from?Where do the formulas come from?

Cylinder Surface Area FormulaCylinder Surface Area FormulaTop πr2

Bottom πr2

Middle Length x width = C x h2πr x h

TotalTotal πr2 + πr2 + + 2πr x hSurface Surface

Area Area FormulaFormula

2πr2 + 2πrh

http://www.brightstorm.com/d/math/s/geometry/u/area/t/surface-area-of-cylinders

Questions AnswersQuestions AnswersWhat is the

formula for the surface area of a

rectangular prism ?

SA =(2 x l x w) + (2 x w x h) + (2 x l x h)

What is the surface area of a

cylinder?

What is the formula for the

surface area of a cube?

SA = 6s2

3 m

5 m

2 m SA = (2 x l x w) + (2 x w x h) + (2 x l x h) SA = (2 x 3 x 2) + (2 x 2 x 5) + (2 x 3 x 5)SA = 12 + 20 + 30SA = 32 + 30 = 62 m2

3 in.

SA = 6s2 SA = 6 x 32 = 6 x 9SA = 54 in2

SA = 2TTr2 + 2TTrh

4 cm

2 cm SA = 2TTr2 + 2TTrhSA = 2 x 3.14 x 22 + 2 x 3.14 x 2 x 4 SA = 6.28 x 4 + 6.28 x 8SA = 25.12 + 50.24 = 75.36 cm2

Surface Area of a PrismSurface Area of a PrismSA = 2(lw) + 2(hl) + 2(hw)SA = 2 x 8 x 6 + 2 x 7 x 8 + 2 x 7

x 6SA = 2 x 48 + 2 x 56 + 2 x 42SA = 96 + 112 + 84SA = 208 + 84SA = 292 ft2

8 ft

7 ft

6 ft

Now you try:Now you try:

What is the surface area of a rectangular prism with a What is the surface area of a rectangular prism with a length of 6 ft, a width of 5 ft, and a height of 7 ft ?length of 6 ft, a width of 5 ft, and a height of 7 ft ?

SA = 2(6 x 5) + 2(7 x 6) + 2(7 x 5) = 214 ftSA = 2(6 x 5) + 2(7 x 6) + 2(7 x 5) = 214 ft22

Surface Area of a CylinderSurface Area of a CylinderSA = 2SA = 2ππrr² + 2² + 2ππrrhhSA = (2 x 3.14 x 3²) + (2 x 3.14 x 3 x 5)SA = (2 x 3.14 x 3²) + (2 x 3.14 x 3 x 5)SA = (6.28 x 9) + (6.28 x 15)SA = (6.28 x 9) + (6.28 x 15)SA = 56.52 + 94.2SA = 56.52 + 94.2SA = 150.72 in² SA = 150.72 in²

3 in

5 in

Now you try:Now you try:Find the surface area of a cylinder that has a height of 5 ft and a radius of 2 ft.

SA = (2 x 3.14 x 2²) + (2 x 3.14 x 2 x 5) = SA = (2 x 3.14 x 2²) + (2 x 3.14 x 2 x 5) = 87.92 ft87.92 ft22

Plug and Chug PracticePlug and Chug PracticeFind the surface area of the following solids using Find the surface area of the following solids using

the appropriate formula.the appropriate formula.1) 1) 2) 2)

3) The side of a cube is 2 cm. What is its surface 3) The side of a cube is 2 cm. What is its surface area?area?

4) You design an oatmeal container as a cylinder 4) You design an oatmeal container as a cylinder with a radius of 2 in. and a height of 22.8 in. with a radius of 2 in. and a height of 22.8 in. What is its surface area?What is its surface area?

12 in.

5 in.2 in.

4 ft.

7 ft.SA = 188 in2

SA = 276.32 ft2

SA = 24 cm2

SA = 312 in2

March 15, 2011March 15, 20111) Write your homework in your agenda: 1) Write your homework in your agenda: Surface Area worksheetSurface Area worksheet2) Open your agenda to your behavior 2) Open your agenda to your behavior

card.card.3) Open your HWP wkbk to Lesson 10-9 3) Open your HWP wkbk to Lesson 10-9

and leave it on your desk.and leave it on your desk.4) Graph your Computation Challenge.4) Graph your Computation Challenge.

HWP Lesson 10-9HWP Lesson 10-9

1)1) s = 600 ins = 600 in22

2)2) s = 268 fts = 268 ft22

3)3) s = 297 fts = 297 ft22

4)4) s = 228 ms = 228 m22

5)5) s = 571.48 cms = 571.48 cm22

6)6) s = 326.56 ins = 326.56 in22

7)7) Pi is an estimated valuePi is an estimated value8)8) 10 ft10 ft22