honors geometry 22/23 february 2012
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Honors Geometry 22/23 February 2012. Warm Up 1. A tall fir tree casts a shadow that measures 8 ½ yards at the same time a six foot man casts a 2 ½ foot shadow. What is the height of the fir tree? a) 20.4 ft b) 61.2 ft c) 63.75 ft d) 153 ft - PowerPoint PPT PresentationTRANSCRIPT
Honors Geometry 22/23 February 2012Warm Up1. A tall fir tree casts a shadow that measures 8 ½
yards at the same time a six foot man casts a 2 ½ foot shadow. What is the height of the fir tree?
a) 20.4 ft b) 61.2 ft c) 63.75 ft d) 153 ftShow your work and explain how you know you are
correct.
2. Find r if C = a) 8.5 in b) 11 in
ObjectiveStudents will find surface area and volume of various
figures.
Students will take notes, participate in class discussion and use think-pair-share.
due TODAYdue TODAYHW grade: TEST CORRECTIONSHW grade: TEST CORRECTIONS
FORMAT:FORMAT:1) Explain what you did incorrectly1) Explain what you did incorrectly
2) rework the problem correctly2) rework the problem correctlyshowing all stepsshowing all steps
3) ATTACH corrections to test paper3) ATTACH corrections to test paper
DO pg. 533: 1, 7, 12DO pg. 533: 1, 7, 12Due February 24Due February 24
Worksheet SA of Cylinders and ConesWorksheet SA of Cylinders and Cones# 1- 6, 9, 10, 12, 13- # 1- 6, 9, 10, 12, 13- show work on separate papershow work on separate paper
VOLUME and SA
BASICALLY,
SA = AREASA = AREAbase(s)base(s) + LSA + LSA (add the areas of the faces)
VVPRISM/CYLINDERPRISM/CYLINDER = A = ABASEBASE x HEIGHT x HEIGHT
HEIGHT is ALWAYS PERPENDICULAR distance
Which has more volume?more surface area?
You can make two different cylinders by rolling a piece of notebook paper either “longways or shortways”. WHICH SHAPE HAS MORE VOLUME?WHICH SHAPE HAS MORE Surface Area? (including the bases?) Can you explain why?
Geometric SolidsGeometric Solids 2 Bases2 Bases 1 Base1 Base No BaseNo Base
Prisms & Prisms & CylindersCylinders Cones & Cones &
pyramidspyramidsSpheresSpheres
Bases are congruent and parallel
Volume = Surface Volume = Surface Area Area The sum of the areas The sum of the areas
of all the facesof all the faces
The ‘outside’ of the The ‘outside’ of the geometric figuregeometric figure
Use area formulasUse area formulas
Measured in square Measured in square inches, square feet…inches, square feet…
COUNT SQUARESCOUNT SQUARES
The measure of the The measure of the amount of space amount of space
contained in a solidcontained in a solid
The ‘inside’ of the The ‘inside’ of the geometric figuregeometric figure
Use volume formulasUse volume formulas
measured in cubic measured in cubic feet, cubic inches…feet, cubic inches…
COUNT CUBESCOUNT CUBES
Oblique Rectangular
Prism
Altitude = heightAltitude = height
Oblique CylinderAltitude = heightAltitude = height
Right Cylinder
Altitude
Term Definition ExampleVolume The measure of the amount
of space contained in a solidMeasured in cubic units
Prism/cylinder volume
conjecture
The volume of a prism or a cylinder is the area of the
base multiplied by the height V = ABASE∙ H
Volume
VolumeVolume
6
BASE is a TRAPEZOID! PRISMS have TWO bases that are PARALLEL and CONGRUENT
V = Abase∙H = ½ (b1 + b2) h ∙ H
V = ½ (10 + 34) (6) (20) = 2640 u3
VolumeVolume RectangularPrism
Triangular prism
2base r
H
base l w wl
H
Trap
ezoi
dal
pris
m
2b hbase
H
1 2
2h b b
base
H
V = AV = Abasebase∙ H∙ H
what about a cone?
DEMONSTRATION--- How many “conefuls” of water will it take to fill a cylinder of the same radius and height?
same height
congruent bases
same volume?
what about a pyramid?
DEMONSTRATION--- How many “pyramids-fuls” of water will it take to fill a prism with same base area and height?
same height
same base areasame volume?
Stud
y Sh
eet
VolumeVolume RectangularPrism
Triangular prism
2base r
Hbase l w
wl
H
Trapezoidal prism
12
base bh
H
1 212
base h b b
HCylinder Prism
Pyramid
2base r
Cone
V = AV = Abasebase∙ H∙ H
V = 1/3 Abase∙ H V = 1/3 Abase∙ H
practice
Complete problems on handout.Be prepared to share them with the class.
You have 25 minutes. This work will be collected for a classwork grade.
debrief
how is volume different that surface area?
how do you find the surface area of a cone? how did we find the volume formula for a cone? a pyramid?