raakri

=rakr317= = = =Chapter 7.= =7.1=

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

__Surface Area and Volume Formulas :__

 * Right Rectangular Prism**-



The surface area, //S// and volume, //V// with length, //l//, width, //w//, and height //h// are
 * __S__** **: 2//lw// + 2//wh// + 2//lh// AND __V__ :** **//lwh//**

The surface area, S and volume, V of a cube with side, //s,// are
 * Cube-**
 * __S__ :** **6//s////²// and __V__ :** **//s////³//**

//page 434 #12-26// :
 * Length || Width || Height || Surface Area || Volume || __Surface Area__ Volume ||
 * 2 || 2 || 1 || **12.) 16** || **13.) 4** || **14.) 4** ||
 * 4 || 4 || 1 || **15.) 48** || **16.) 16** || **17.) 3** ||
 * 7 || 4 || 5 || **18.) 166** || **19.) 140** || **20.) 1.2** ||
 * 4 || **21.) 7** || 3 || **22.) 122** || 84 || **23.) 1.45** ||
 * 2 || 5 || **24.)** **6** || 104 || **25.) 60** || **26.) 1.7** ||

=**7.2**=

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


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

Surface Area of a Right Prism
The surface area, //S//, of a right prism with lateral area //L//, base area //B//, perimeter //p//, and height //h// is __**S**__ =L +2B __OR__ __**S**__= hp + 2B

What is Cavalieri's Principle?
If two solids have equal heights and the cross sections formed by every plane parallel to the bases of both solids have equal areas, then the two solids have equal volumes.



7.3
(http://interoz.com/egypt/construction/head.gif) A polyhedron containing a base, and three lateral faces. A polygon The equal length from the altitude(Of a pyramid) Lateral faces all go to a vanish point and meet at a single vertex. Where two lateral faces meet or cross. Common edges within lateral faces The perpendicular Segment from the point of vertex to the plane of the base[Of a pyramid]. A regular polygon equals its base. Congruent Isosceles triangles equal lateral faces. All lateral edges are equal to each other, the altitude crosses the base at its center. Altitude length of lateral faces.
 * Pyramid:**
 * Base:**
 * Height:**
 * Vertex of the Pyramid:**
 * Lateral Edge:**
 * Base Edge:**
 * Altitude:**
 * A Regular Pyramid:**
 * The Slant Height:**

Surface area of a regular pyramids:
S : L + B OR S =1/2 lp + B

Volume of a regular pyramid:
V : 1/3 Bh

7.4
(http://www.xvrml.net/images/cylinder.png) A cylinder is a complete solid circular object, think of a can of soup. It's image that is reflected across is on a parallel plane, with a //Lateral Surface attaching the top to the bottom.// The circular region form faces of the cylinder A segment connecting the top to the bottom. The curved surface of a cylinder or cone Equals the altitude. The segment in the center of the top and bottom, connecting the entire object together Axis isn't perpendicular If not a right cylinder, then its oblique.
 * Cylinder:**
 * Bases:**
 * Altitude:**
 * Lateral Surface:**
 * Height:**
 * Axis:**
 * Right Cylinder:**
 * Oblique Cylinder:**

Surface area of a right cylinder:
S : L + 2B -or- S= 2(pi)rh+2(pi)r²

Volume of a cylinder:
V : Bh -or- V= (pi)r²h

7.5
([|http://www.cs.vu.nl/~eliens/documents/vrml/reference/IMAGES/CONE.GIF]) It is 3 dimensional, that has a circular base on the bottom. A curved lateral face runs up and down the right and left sides, connecting the entire shape together, to the base.The point where everything meets is the vertex. If the height, or altitude crosses the base of the cone in the middle. Equals the altitude The perpendicular line running down the middle connecting the vertex to the base
 * Cone:**
 * Right Cone:**
 * Height:**
 * Altitude:**

S : L + B -or- S= (pi)rl + (pi)r²
 * SA of a Cone:**

V : 1/3 Bh -or- V= 1/3 (pi)r²h
 * V of a Cone:**

7.6
(http://www.web3d.org/x3d/specifications/vrml/ISO-IEC-14772-VRML97/Images/sphere.gif) There is one center point in the middle of the sphere, every point around the circle has the same distance, or radius.
 * Sphere:**

S : 4(pi)r2
 * Surface area of a sphere:**

V : 4/3(pi)r3
 * Volume of a sphere:**

=__FORMULAS --__= 1. Volume of a Trianular Prism 2. Surface Area of a Triangular Prism 3. Volume of a Pyramid 4. Surface Area of a Pyramid 5. Volume of a Cylinder 6. Surface Area of a Cylinder 7. Volume of a Cone 8. Surface Area of a Cone 9. Volume of a Sphere 10. Surface Area of a Sphere
 * BH**
 * L+2B or HP+2B**
 * (1/3)BH**
 * L+B or (1/2)//l//P+B**
 * BH or (pi)r//²// h**
 * L+2B or 2(pi)rh + 2(pi)r²**
 * (1/3)BH or (1/3)(pi)r//²// h**
 * L+B or (pi)r//l// + (pi)r//²//**
 * (4/3)(pi)r³**
 * 4(pi)r//²//**

= = =Chapter 8.= =8.1=