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=__Section 1 Surface Area and Volume__=

**OBJECTIVES:**

 * Develope the concepts of maximizing volume and minimizing surface area.

SURFACE AREA AND VOLUME DEFINITIONS


 * Surface Area of an Object-** //The total area of all the exposed surfaces of the object//.
 * Volume of a Solid Object-** //The number of nonoverlapping unit cubes that will exsactly fill the interior of the figure//.

FORMULAS FOR SURFACE AREA AND VOLUME The surface area (S) and volume (V) of a right rectangular prisim with length L, width W, and height H are //S=2LW+2WH+2LH and V=LWH// A picture below as an exsample: The surface area (S) and the volume (V) of a cube with the side labeled S are A picture below as an exsample: ** //A WEBSITE THAT SHOWS YOU HOW TO GET THE SURFACE AREA AND VOLUME OF MANY DIFFERENT [|SHAPES.]//
 * __(2 and 3 are squared)__
 * //S=6s2 adn V=s3//

An Example:
 * A soap degergent company is trying to make a decison on what size box to use. What box has the most surface area and thus requires more material for the same volume?**

BOX A ..............................................BOX B //BOX A: S=2(5)(2)+2(2)(10)+2(5)(10) 20+40+100=**160**

BOX B: S=2(10)(1)+2(1)(10)+2(10)(10) 20+20+200=**240**//

=__Surface Area and Volume of Prisms Section 2__=

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 Cavilieri's Principle to develope a formula for the volume of a right or oblique prism.//


 * Altitude of a Prism**- a segment that has endpoints in the planes containing the bases and that is perpendicular to both planes.
 * Height of a Prism**- is the length of an altitude.

**Surface Area of a Right Prism:**
> S=L+2B or S=hp+2B**
 * **surface area (s)**
 * **lateral area (l)**
 * **base area (b)**
 * **perimiter (p)**
 * **height (h)

//A cool website about [|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.//

//**Pyramid:** is a polyedron consisting of a base, that is a polygon, and three or more lateral faces.
 * Vertex of the Pyramid:** The lateral faces are triangles that share a single vertex.
 * Base edge:** Each lateral face has one edge in common with the base.
 * Lateral edge:** The intersection of two lateral faces.
 * Altitude of a Pyramid:** the perpendicular segment from the vertex to the plane of the base.
 * Height of a Pyramid:** is the length of its altitude.
 * Regular Pyramid:** is a pyramid whose base is a regular polygon and whose lateral faces are congruent isosceles triangles.
 * Slant height of a Pyramid:** The length of an altitude of a lateral face of a regular pyramid.//

Surface area (s) Lateral area (L) Perimeter of a base (p) slant height (l)
 * //Surface Area of a Regular Pyramid://**

__FORMULA:__

S L+B or S1/2lp+B
A platform of a deck is a regular hexagon pyramid with a base edge of 6 feet and a slant height of 8 feet. Find the area of the deck. If deck material costs $4.50 per square foot, find teh cost of covering the deck with this material. L=1/2lp= 1/2(8)(5*6)=120 120* $4.50 per square foot = $540.//
 * Example** //of the Surface Area of a Regular Pyramid-

//**Volume of a Pyramid:** Volume (v) Height (h) Base area (B)//

//V=1/3Bh//

One of the ancient egyptian pyramids is a regular square pyramid with a base edge of 660 feet and an original height of 310 feet. The gold used to construct the pyramid weighs 160 pounds per cubic foot. Estimate the weight of the pyramid of the pyramid. (the pyramid is solid)
 * Example** //of Volume of a Pyramid:

V=1/3Bh =1/3(660squared)(310)//

__Surface Area and Volume of Cylinders Section 4__ //Objectives://
//**Cylinder:** A cylinder is a solid that consists of a circular region and its translated image on a parallel plane.
 * //Define and use a formula for the surface area of a right cylinder.//
 * //Define and use a formula for the volume of a cylinder.//
 * __VOCAB.__**
 * Lateral Surface:** connects the circles
 * Bases of the Cylinder:**The faces formed by the circular region and its translated image.
 * Altitude of a Cylinder:** is a segment taht has endpoints in the planes containing the bases and its perpendicular to both planes.
 * Height of a Cylinder:** is the length of an altitude.
 * Axis of a Cylinder:** is the segment joining the centers of the two bases.
 * Right Cylinder:** the axis of a cylinder is perpendicular to the bases.
 * Oblique Cylinder:** the asis of a cyilinder is not perpendicular to the bases//.

Surface area (s) Lateral area (L) base area (B) Radius (r) height (h
 * __Surface area of a right cylinder__**

S = L + 2B
 * Formula:**

OR

S = 2piRH + 2piR2(squared)

//__Example:__//

//A nickle is a right cylinder with a diameter of 15.5 millimeters and a thickness of 2.25 milimeters. Forget the raised design, estimate the surface area of the penny.

SOLUTION://

Volume (v) Radius (r) Height (h) Base area (b)**
 * __Volume of a cylinder__

V = Bh
 * Formula:**

Or

V = piRsquaredH

__Surface Area and Volume of Cones Section 5__
//Objectives:// VOCAB. //**Surface Area of a Right Cone-**// Base of area (b) radius (r) Height (l)//**
 * //Define and use the formula for the surface area of a cone.//
 * //Define and use the formula for the volume of a cone.//
 * //**Cone-** is a three-demensiosal figure.//.
 * //**Base-** circular base//
 * //**Lateral surface area-**Lateral surface area- connects the base to a single point in the plane of the base.//
 * //**Vertex-**Vertex- the base that connects the base to a single part//
 * //**Altitude of a cone-**Altitude of a cone- the perpendicular segment from the vertex to the plane of the base.//
 * //**Height of the cone-**Height of the cone- is the length of the altitude.//
 * //**Right cone-**Right cone- If the altitude of a cone intersects the base of the cone at its center.//
 * //**Oblique cone-**Oblique cone- if the altitude of a cone doesn't intersect the base of the cone at its center.//
 * //Surface area (s)//**
 * //Surface area (l)

Lateral area (l) Base (b) Radius (r) Slant height (L)
 * //Volume of a Cone-//**
 * //Surface area (s)

Formula: S=L+B or

S=pirL+pir2//**

Volume (v) Radius (r) Height (h) Base (b)
 * //Volume of a cone-

V = 1/3Bh OR V=1/3pir2h//**

//[[image:1204270650_7c9d1e2796.jpg width="332" height="322" link="http://www.flickr.com/photos/cobalt/1204270650/sizes/m/"]] Objectives://

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

Volume of a Sphere Volume (V) Radius (r) V=4/3pir3 EXAMPLE: //The envelope of a hot air balloon has a radius of 30 feet when fully inflated. Approximately how many cubic feet of hot air can it hold?// //=4/3pi(30)3// //=4/3(27000)pi// //=113097.33 cubic feet = 56548.66//
 * Sphere**: Is the set of all points in space that are the same distance,r, from a given point known as the center of a sphere.

Surfacearea (s) Radius (r) s=4pir2 //Example:// //The envolope of a hot-air balloon is 60 feet in diameter when inflated. The cost of athe faberic used to make the envelope is 2.00 per square foot. Estimate the total cost of the fabric for the balloon envelope.// //SOULUTION:// //=4pi(30)2// //=4(900)pi// //=3600pi=11309.73 square feet//
 * Surface area of a sphere:**

//Objectives://

 * //Define various transformations in three-demensional space.//
 * //Solve problems by using transformations in three-demensional space.//

Three-demensional figure may be reflected across a plane, just as a two-demensional figure can be reflected across a line.