selgra

=SE GR 5 22= chapter 9 link!

=Chapter 7.1 Surface Area & Volume=

Objectives
 * Explore ratios of surface area to volume.
 * Develop the concepts of maximizing volume and minimizing surface area

-IMPORTANT FORMULAS-
Surface Area (S) = **2lw + 2wh +2lh** Volume (V) = **lwh**
 * Right rectangular prism**

Surface Area (S) = **6s²** Volume (v) = **S³**
 * Cube**

S= surface area V= volume l= length w= width h= height

EXAMPLE- **Q.** While your wrapping a present for your extravagant math teacher you notice that your really low on wrapping paper. How to you measure out how much you need to compoletly cover the present?
 * A.** Use the surface area formula (2lw+ 2wh+2lh) to measure out how much you need.
 * Q.** You are starving so you make a quick run to the grocery store and on your way to the cereal section your can of baked beans falls out. What should you do to fit everything into that tiny shopping cart?
 * A**. Use the volume formula (lwh) to maximize the amout of items your cart can fit.

=Chapter 7.2 Surface Area & Volume of Prisms=

Objectives
 * Define and use a formula for finding the surface area of a right prism.
 * Define and use a formula for finding the volume of a right prism.
 * Use Cavalieri’s Principle to develop a formula for the volume of a right or oblique prism.

-IMPORTANT VOCABULARY-
Altitude- A segment that has endpoints in the planes containing the bases and is perpendicular to both planes. Altitudes are found in all prisms. Height- The length of an altitude of a polygon.

Cavalieri's Prinicple- If two solids have equal heights and the cross section formed by every plane parallel to the bases of both solids have equal volumes.

-IMPORTANT FORMULAS-
Surface Area (S)= **L+ 2B** OR Surface Area (S)= **hp+2B
 * Surface Area of a Right Prism**

Volume of a Prism** Volume (V)=**Bh**

To find the lateral areas of prisms it may help to use a //net// If the sides of the base re S1, S2 and S3 and the hight is h

L= S1h+ S2h+ S3h = h(S1+ S2+S3)



EXAMPLES- **Q.** After a year of camping you and your friends are ready to pack up and move to a different site. But before you can travel you need to pack the tent up. How will you know if you have enough room to completly deflate the tent to wrap it up without running into a type of shrubbery?
 * A.** Using the surface area of a prism formula (L+2B) you can find out how much space the tent covers and then if its too large you can pick it up and move it into a wider, more open clearing.

=7.3 Surface Area and Volume of Pyramids=

Objectives
 * Define and use a formula for the surface area of a regular pyramid
 * Define and use a formula for the volume of a pyramid.

-IMPORTANT VOCABULARY-
Pyramid- A polyhedron in which all but one of the polygonal faces intersect at a single point known as the vertex of the pyramid. Base- The polygonal face that is opposite the vertex. Lateral Face- the face of a prism or pyramid that are not bases. Vertex of the Pyramid- The point where all the lateral faces of the triangle share. Base Edge- An edge that is part of the base of a pyramid; each lateral face has one edge in common with the base. Lateral Edge- The intersecton of 2 lateral faces of a polyhedron. Alititude- A segment from the vertex perpendicular to the plane of the base. Height- The length of an altitude of a polygon. Regular Pyramid- A pyramid whose base is a regular polygon and whos lateral faces are congruent isosceles triangles. Slant Height- In a regular pyramid, the length of an altitude of a lateral face.

EXAMPLE- **Q.** On the day after Thanksgiving you get up at 5 to shop for some Christmas Tree lights. At the store your getting pushed about by the massive crowds and you have to hurry and decide how many tree lights you want. How would you go about thinking this?
 * A.** You could use the surface area formula to figure out how much space you will need to cover in lights.

FuNkÈ FÃcTs
Pyramids (and prisms) are named after the shape of their base. -Triangular Pyramids - Rectangular Pyramids - Pentagonal Pryamids - Hexagonal Pyramids

-IMPORTANT FORMULAS-
Surface Area (S)= L+B OR Surface Area(S)= 1/2lp+B
 * Surface Area of a Regular Pyramid**

L=lateral Area B= Base area l=slant height p=perimeter of base

Volume(V)= 1/3 Bh
 * Volume of a Pyramid**

h= height B=Base Area

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=7.4 Surface area and Volume of Cylinders= Objectives
 * Define and use a formula for the surface area of a right cylinder.
 * Define and use a formula for the volume of a cylinder.

-IMPOTANT FORMULAS
Surface Area(S)= L+2B OR Surface Area(S)= 2xPi //(3.14)// rh+2xPi //(3.14)// r²
 * Surface Area of a Right Cylinder**

Volume(V)= Bh OR Volume(V)= Pi //(3.14)// r²h
 * Volume Of a Cylinder**

EXAMPLE- **Q.**Betty and Mary-Jo want to split a soda but Betty picks fights alot, so Mary-Jo wants to split it exactly even, thus avoiding arguments. How what is exactally half of their soda. (diameter of can= 5 Height of can 8= )
 * A.** 157units³ is in the whole soda can. Betty will recieve 78.5units³ and Mary-Jo will recieve 78.5units³ also.

-IMPORTANT VOCABULARY-
Cylinder- A solid that consists of a circular region Lateral Surface- Is a translated image on a perallel plane connecting the circles. Bases- Faces formed by the circular region and its translated image. Altitude- A segment that has endpoints in the planes containing the bases and its perpendicular to both planes. Height- Length of altitude. Axis- The segment joining the centers of the 2 bases Right Cylinder- If axis of cylinder are pependicular to the bases Oblique Cylinder- If not a right cylinder (above) then it is this. -oblique-

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FuNkÉ fÃcTs
The more sides of a regular polygon the quicker the figure becomes more like a circle

=7.5 Surface Area and Volume of Cones= Objectives
 * Define and use the formula for the surface area of a cone.
 * Define and use the formula for the volume of a cone.

-IMPORTANT VOCABULARY-
Cone- A 3-Dimensional figure that consists of a circlular base. Base- The circular face of the cone. Lateral Surface- The Curved surface of the cylinder or cone. Alititude- A segment from the vertex perpendicular to the plane of the base. Height- The length of an altitude of a polygon. Right Cone(pictured above)- A cone in which the altitude intersects the base at its center points. Oblique Cone(pictured above)- A cone that does not fit the definition of a right cone (above) Slant Height of a Cone- The sector's radius of a net.



-IMPORTANT FORMULAS-
Surface Area(S)=L+B OR Surface Area(S)= Pi //(3.14)// rl+ Pi //(3.14)// r²
 * Surface Area of a Right Cone**

Volume(V)= 1/3Bh OR Volume(V)=1/3xPi //(3.14)// r²h
 * Volume of a Cone**

=7.6 Surface Area and Volume of Spheres=

Objectives
 * Defineand use the formula for the surface area of a sphere.
 * Define and use the formula for the volume of a sphere.

-IMPORTANT VOCABULARY-
Sphere-The set of points in a spacethat are equidistant from a given point known as the center of the sphere. Annulus- The region between 2 circles in a plane that have the same center but different radii.

-IMPORTANT FORMULAS-
Volume(V)= 4/3xPi //(3.14)// r³
 * Volume of a Sphere**

Surface Area(S)= 4xPi //(3.14)// r²
 * Surface Area of a Sphere**

FuNkÉ fÃcTs
To find the volume of a sphere we must first show that a sphere has the same volume as a cylinder with a double cone cut out of it



EXTRA!!

 * GET YOUR EXTRA EXAMPLES**

//1.// //Volume of a triangular prism//

Find the volume of a triangular prism with the demensions L=5 W=3 H=2

//2. Surface area of triangular prism//

You got a new job making Toblerone chocolates. You are in charge of the wrapping before they get shipped out...for one of the EXtra huge chocolate bars with the Lenght of 3inches the hight of 1inch and the width of 4inches how much tinfoil will each need to be wrapped?

//3. Volume of pyramid//

Its your 49th birthday and your really into pinyatas, for that special day you want one shaped like a unicorn horn. But how will you know how much candy to put in a pyrimid shaped figure with the height of 14inches a length of 10inches and width of 17inches

//4. Surface area of pyramid//

Your old yard knome needs repainting on his hat that has a lateral area of 4, lenth is 5 and width is 7,how much square inches will you paint? you may have enough paint left over for his slacks!

//5. Volume of cylinder//

In the 90's you had your cylinder tube for your pogs, now they are comming back in style and you have a new tube that is 4inches in hight and has a diameter of 4inches. Will you have room for lots of pogs? How much room?

//6. Surface area of cylinder//

During school you need to make a video but you absolutly cannot have any advertisements, QUICK cover your pop can with the 6cm diameter and the 20cm height with a piece of paper!

//7. Volume of cone//

Mmm... ICE CREAM how much can you pack into a small cone 4inches tall with the diameter being 6inches?

//8. Surface area of cone//

Time for some homemade party hats! Your friends heads are 8inches in diameter and they need to be 5inches for the lateral area. How many pieces of fun paper will you need?

//9. Volume of a sphere//

Hitting up the beach when you notice your beach ball is competly flat! How much air will you need to pump into a ball that has the diameter of 20inches?

//10. Surface area of a sphere//

Your old lucky baseball needs to be recovered because it ripped. You will pay as much as it costs to completly cover a baseball that is 5inches across. How much covering will the store need?

answers to the examples
1.) 30units3 2.) 27inches2 3.) 793 inches3 of candy! 4.) 140units2 5.) 50inches3 for your pogs 6.) 433cm2 7.) 37inches3 8.) 113inches2 9.) 4188inches3 of air 10.) 78inches2 of new covering

__HAPPY- HONORABLE - HELPFUL LINKS!!!__
http://argyll.epsb.ca/jreed/math9/strand3/3107.htm a fun site to help you review over volume, area, surface area for pyramids, prisms cylinders..etc

http://thinkzone.wlonk.com/Area/AreaVol2.htm this will help you understand the shapes better and how to find their volume.

http://mathforum.org/dr.math/faq/formulas/faq.cylinder.html Dr.Math will help you with cylinders!

http://library.thinkquest.org/20991/geo/solids.html#spheres Need more help on spheres? prisms? cone? click here and scroll to your weakest topic.

http://math.about.com/library/blmeasurement.htm Formulas for every shape you can imagine!