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