April 17,2012

Aim:  How do we find the volumes of pyramids and cones?

Volume formula for the pyramid and cone :

V: 1Bh                                                                  
       3
                                                                     
For the volume for pyramid and the cone you have to divide by three.

      In the formula for the pyramid the B stands for the area of the base.

       

In this case the base is a square so to find the area of the base we would use the length of the square and multiply it by its self so : length of one side <sup>2 .
After that multiply it by the height and divide it by three.

Cone: 
The cone can have the same formula as the pyramid but it can also be shown this way :</sup>
 V: 1πr2H

        3     






 πr2 is used instead of the area of the base which is a circle.


^{try it :}
 

	Choose:  2,095,533 20,955,334  43,442,812 74,350,037
The Pyramid of Khafre was built for the son of Khufa, for whom the Great Pyramid was built.  It is slightly smaller in size than the Great Pyramid. The height is 447.5 feet. The base side length is 706 feet. Find the volume of the Pyramid of Khafre to the nearest cubic foot.

^{images:  http://regentsprep.org/Regents/math/geometry/GG2/PyramidPage.htm
 http://regentsprep.org/Regents/math/geometry/GG2/ConePage.htm}
Try it : http://regentsprep.org/Regents/math/geometry/GG2/PracSol.htm

April 18,2012

Aim: How do you find the surface area and volume of a sphere?

fist of all :)
what are spheres?
         A sphere is a figure that holds all set of points in space that are equidistant from a given point
                                           
To find the volume of the sphere you need to use the formula :
            V= 4πr3
                      3
 for example:
in a sphere we have a radius of 4,find the volume and leave it to the nearest tenth


First we plug in things we know :
 V= 4π43
            3
Next:
we  solve the exponent and multiply the number :
 V= 4π64  = 256π  
          3           3
Then :
tell  divide the number and leave π there 
the final answer is :

v = 85.33π

to find the Surface area the formula is  : 

SA: 4πr2

Ex: a sphere has a radius of 4find the surface area:

First plug in everything you know:

SA: 4 π42

Next:solve what the exponents and also multiply by 4

4* π*16=  64*π

 Finally : 

your answer can be left as terms of π or to the nearest tenth. 

64π or 201.1

TRY IT :D

1.		Soda is sold in aluminum cans that measure 6 inches in height and 2 inches in diameter.  How many cubic inches of  soda are contained in a full can? (Round answer to the nearest tenth of a cubic inch.)	Choose: 12.0 18.8 24.0 75.4

sources used:

regents prep: 

http://regentsprep.org/Regents/math/geometry/GG2/PracSol.htm

 Google images:http://knowledgepublications.com/doe/images/DOE_Mathematics_Sphere.gif

March 28,2012


Aim:How do we find the surface area and lateral area of a cylinder?


To find the surface area of a cylinder we first need a formula.





when having the formula we then apply it to the cylinder.
A cylinder has two bases that are circles.
if we didnt know the equation we could solve the area for the circle and multiply it by 2 since there is two circles.


After we have the area of the circle we then have to find the area of the other part of the cylinder which is called the lateral area. The lateral area and the area of the two bases are the total surface area.




For example:
     
2= raduis
6= height


To find the total surface area we need the formula.
SA= 2πrh+2πr ²


PLUG IN:
SA= 2*π*2*6+ 2*π*(2) ²

Solve parts of the equations.( leave in terms of π if told so)
SA= 2πrh
2* π*2*6
2*2*6= 24 
add the π 


 First part of the equation would be: 24π


Second part of the equation:
SA= 2πr ²
2*π*(2)2
(2)2 =4
so 4*2= 8
 plus π
answer to the second half: 8π

ADD them together and the answer would be 30 π 
          
NOW YOU TRY:D


A cylinder has a height of 8 and a radius of 4 
find the surface area.
leave in terms of π.

SOURCES USED:
http://www.mathwarehouse.com/solid-geometry/cylinder/images/cylinder-area-problem1.jpg
http://www.regentsprep.org/regents/math/algebra/AS2/Solids.htm

March 26,2012

Aim:How do we identify solids ?

Do Now:

Are these solids ?

            

A solid is a  3 dimensional figure that has volume as well as the surface area.

If you didnt know :

volumen is the inside of the figure :)

and the surface area is the outer region of the figure ;)

there's two types of solids:)

one is named "polyhera" and the other is "non-Polyhedra"

A polyhera solid is a solid that must have flace surfaces or face.

examples of polyhedra solids are 

• pyramids
• prisms
• platonic solids

Non-Polyhedra:

are figures that don't have a flat surface .

examples of non-polyhedra figures are:

• cylinder
•  torus
  
• Cone

TRY it :D

Is a rectangle a polyhedra or a non-polyhedra?

1)yes

2) maybe

3) no 

sources used:

http://msnucleus.org/membership/html/k-6/rc/minerals/3/images/rc3m06.gif

http://mathpalette.com/wp-content/uploads/2012/02/donut-torus.png

http://www.chileunderground.com/wp-content/uploads/2012/02/MagicSphere.png

http://www.rhythmsoftheglobe.com/gr/images/bpd/pyramid.jpg

http://aws-item-images.artfulhome.com/item_images/P/8201-8300/large/P08257-P00005l.jpg

MARCH 20,2012
AIM: HOW DO WE FIND THE AREA OF A CIRCLE ?
To find the area of the circle we need to use the formula: 
A= πr2
In the circle 
to find the area we need to know the radius 
at times the radius might not be given to us but since the diameter is twice of the radius we divide the diameter by 2.


For example:
           FIND THE AREA !

To find the area we need to know the radius but it isnt given to us. in that case like i said before divide the diameter by 2 to get the radius,
10/2 = 5 
the radius turns out to be 5.
when you have the radius then plug it in the formula: A= πr2
Next plug it in :
A=π(5)2
Do the exponent :
A=π (25)
final answer:
A=π25


Leave the answer in the pi form because with pi the answer is accurate. If you are to to round to the nearest tenth then round otherwise leave it as in form of pi.

you try:

Jessica is making a circular table cloth for an art project.  She wants half of the cloth to be a plain colored fabric and half to be a print fabric.  How many square yards of each fabric (to the nearest hundredthof a yard) will she actually be using if the diameter of the cloth is 6 feet?

Choose:  1.57 sq. yds  1.58 sq. yds  14.13 sq. yds  14.14 sq. yds

Sources:

regents prep.org for the you try and the little circle above.

march 19,2012

Aim: How do we find the area of regular polygons ?

STEP 1:
when finding the area of a regular polygon we first need to notice what kind of polygon we are working with.

in the image oin the right is a hexagon.
in the hexangon if a teacher or a person were to say what is the area of the hexagon then look its a hexagon.

STEP 2 : KNOW WHAT AN APOTHEM IS :)

LEts ssay this is a regents problem and thety tell you to find the area of the polygon.First know the formula.

The formula :

NAS

   2
N: number of sides
A: apothem
S: the base
and divide that by 2.





many might not know what an aopothem is :)
so ill tell you :)
an apothem is the distance between the sides of the polygon to the center.
in this case the apothem is 2.

STEP 3:COUNT THE SIDES ! FOR N  :):D
 Like i said before
N is the number of sides
in this case since its a hexagon  there is six sides

like in the image shown in the left ------>















STEP 4: THE S IS NEXT :)
                     
 So from step 2 and step 3 we know that  N ISTHE NUMBER OF SIDES
A IS THE LENGTH BETWEEN THE SIDES AND THE CENTER

THE S :
the s is the base and dont get confuse just because its the base it doesnt mean that its in the bottom the base is anywhere that the number is next to a side.
in this case the s would be 6.

STEP 5: PLUG IT IN !!! YAY ^O^

now that we know what an apothem , n, and s is we can plug the numbers in the formula for area.
SO...... now we apply the new knwodleg we now know and solve the problem :)
ALSO DONT FORGET TO
 SHOW WORK !

FORMULA :
NAS
  2
PLUG IN :
 6*2*6 
    2
multiply first :
6*6= 36*2 =72
THEN DIVIDE:
72 
2
Final answer is
36 because 72/2  is 36
so the final area would be 36.


YOU SHOULD KNOW :
what an apothem is now :)
how to calculate the area of any polygon because the formula:
NAS
  2
works for every polygon


there might be a case where the area was already given to you: in that case plug in the area and dop it like a equation 


for example:
A= 72 
a=6
n=6
find the S


then we plug in the equation 


72= 6*6*s
          2
To get rid of the two in the other side of the equation you multiply 72*2 which equals 144. then also multiply 6*6 which are the other side of the equation. once that's done divide 144/36 which gives us 4 and that would be the S= the base :).


NOW YOU TRY:D

If we have an area of 20 and the apothem of 2 and there are 2 sides what is the S ?

March 15,2012

AIM: How do we find the area of parallelograms, kite and trapezoids ?

PARALLELOGRAM:
To find the area of a parallelogram
is like finding the are of a rectangle .

For the parallelogram we need to first cut a line in the parallelogram where it forms a triangle. in the image to the left parallelogram ABED we cut a line from A to C with that forming triangle we place the triangle to the other side forming a rectangle ACFD.

FORMULA: B x H

-----------------------------------------------------------
 EXAMPLE:

Find the are of a parallelogram with a base of 12 centimeters and a height of 5 centimeters.
First : Apply the formula A=B*H Then : plug in the base and height: A=12*5 solve the equation: A= 60cm2 ------------------------------------------------------------------------------ TRAPEZOID :      Formula :   A= (B1+B2)H                                 2 B stands for base H for height A for area ----------------------------------------------------------------------------- Example:           First:  write the formula : A= ( B1+B2)H             2 Plug in numbers: A= (10+14)5           2 Solve : A=( 24)5          2 A= 120        2 A= 60 in2 ------------------------------------------------------------------------------ Kite: WHAT THE PICTURE SHOWS: it shows the formula for the are of a kite  D1 and D2 of the kite are shown. ------------------------------------------------------------------------------- EXAMPLE: First:  rewrite the formula : A= D1*D2                                           2 SECOND: PLUG IT IN A= D1+D2            2   A= 10*2        2    Solve the equation : A= 20 = 10       2 Answer A=10 ------------------------------------------------------------------------------ TRY IT: Find the area of the kite. Measurements shown are in cm. [Given x = 12 and y = 16.] Sources used : Try it : http://www.icoachmath.com/math_dictionary/Kite.html  kite: http://www.k6-geometric-shapes.com/image-files/formula-area-kite.jpg  Trapezoid:

http://www.mathgoodies.com/lessons/vol1/area_trapezoid.html

Parallelogram:

http://www.google.com/imgres?um=1&hl=en&sa=N&biw=1440&bih=742&tbm=isch&tbnid=04sOwxGuuyV2wM:&imgrefurl=http://www.onlinemathlearning.com/area-parallelogram.html&docid=_D9pX-D7SJI8CM&imgurl=http://www.onlinemathlearning.com/image-files/areas-parallelogram-2.gif&w=223&h=129&ei=iz1mT_CSIObr0gHi1_WPCA&zoom=1&iact=rc&dur=454&sig=107129537430957669125&page=3&tbnh=103&tbnw=178&start=38&ndsp=22&ved=1t:429,r:5,s:38&tx=99&ty=88