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14April 2011 Warm UP– 14April 2011 Warm UP– silently pleasesilently please
1) HOMEWORK DUE NEXT CLASS: pg. 568: 7 – 9 pg. 548: 5, 72) WARM UP- Find the surface area and volume for each:
ObjectiveStudents will be able to find dimensions of a solid when given the volume
and find volume in real world applications.
Homework Due TODAYFinish Volume and Surface area of Geometric Solids Problems- EVENS Include Sketch, formula substitute #’s units
√ or X or -10
2
b h
Area formulas:
b h 1 2
2
h b b 1 2
2
d d
b h
Regular Polygons
2
a s nA
or
2
a PA
Circles
r
2A r2C r
or
C d
2
360
aA r
Circle sectors
ra
a
s
Volume FormulasVolume Formulas
Prism/CylinderPrism/Cylinder
V areaofbase height
Cone/pyramidCone/pyramid
3
areaofbase heightV
SphereSphere34
3
rV
Surface area Surface area of a Sphereof a Sphere
24SA r
Stu
dy
Sheet
VolumeVolume
Rectangular Prism
base h
Triangular prism
2V r h
h
V l w h
V area of
wl
h
Trapezoidal prism
1
2V bh H
H
1 2
1
2V h b b H
HCylinder Prism
Pyramid
1
3V B h 1
3V B h
2( )base B r
Con
e
hh
( )base B l w
hb l w
FINISH PostersSTART by sketching your figure/ writing basic
information CLEARLY on your poster paper.Surface area– clearly show all the “pieces” and area for
each “piece”
REQUIRED- FORMULA substitute #s do the math add units
FINISH with pencil, then I’ll give out markers
Group # 1 2 3 4 5 6 7Problem # 13 9 5 3 1 11 7
Solving for any variable
We can use algebra to rearrange a formula and define it for any variable.
EXAMPLE: A chocolate manufacturer is experimenting with new cylindrical cans for hot-cocoa. The can needs to hold 73 in3. Find the diameters of the can that correspond to heights of 4 in, 5 in, 6 in and 7 inches.
We can rearrange the formula….
Start with what we know: Vcylinder = Abase H = r2 H
and we know that r =
2
d
So start by substituting
V = ( )2 H2
d
Now, let’s solve for d
Remember we evaluate expressions using order of operations. P = parenthesis E = exponents M/D= multiply OR divide A/S = add or subtract
We UNDO by going in the opposite order using the UNDOING operation addition “undoes” subtraction subtraction “undoes” addition multiplication “undoes” division division “undoes” multiplication AND SQUARING “undoes” square roots!!!!
AND remembering the “GOLDEN RULE OF ALGEBRA….
What you do to one side, you gotta do to the other side
V = π ( )2 H 2
d
2( )2dHV
H H
divide both sides by πH
2( )2
V d
H
2
4
V d
H
2
4 44
V d
H multiply both sides by 4
4V
dH
2V
dH
OR
Now you can use this formula to find the can diameters
for H = 4in, 5 in, 6 in, 7 in
Show formula substitute #’s do math units
pg. 568 do # 1 - 6
THINK– silently for 5 minutesPAIR– check with your partnerSHARE– share with class
GROUP WORKA standard juice box holds 8 fluid ounces. A fluid
ounce of liquid occupies 1.8 in3.
DESIGN a cylindrical can that will hold about the same volume as one juice box. What are some possible dimensions of the can?
Find at least two different sizes.
Find the surface area for TWO of your can sizes.Based on cost of the container, with the same
material, which is the most economical container to make?
Application problems
pg. 548: 2, 3, 6
Do all three on your paper to be submitted for classwork.
Remember, sketch, then formula substitute #’s do the math add units