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=//beda218 Chapter 7//=

Surface Area and Volume
1**. Explore ratio of surface area to volume and Surface area and volume ratio is very easy to find however finding each individual part is not. its simply SA/V.
 * //Main Ideas for 7.1//
 * 2.** Understand concepts of having low surface area and maximum volume

//**Formulas**// A rectangular prisms Surface are area is //2LW+2WH+2LH (S=2LW+WH+2LH).// Volume is LWH where L is length W is width and H is the height //(V=LWH).// Cubes are somewhat easier to find, the surface area of a cube is //6s^2 (S=6S^2// Cubes volume is //s^3 (V=s^3// The first formula is good for a any rectangular prisms, including cubes, however the second one while easier and quicker to find is applicable to [|cubes] only. //Finding the surface area to volume is very simple. find the both peices use the surface area as the numerater and the volume as the demonater and you have it. its simply SA/V.//
 * //surface area to volume,//**
 * Example**, find the ration of suface area to volume for a cube with a volume of 50^3. cube root 50=3.68, now 3.68^2(for area of a side) 13.57*6 for surface area=81.43 the surface area. Now just put that over the origanl volume and you have 81.43/50.

=7.2= Main Objectives// 1.** Finding the surface and volume for right prisims //Altitude,//a segment with endpoints in the planes containing the bases and is perpindicular to both of the planes //Height,// the length of the altitude. //**Formulas**// Surface area of a right prism, //s=l+2b or s=hp+2b// Volume of a prism, //v=bh// [|Cavalieris principle],if two silids 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//.//
 * //Surface Area and Volume of Prisms
 * 2.** Use a formula to find the volume of a right prism
 * 3.** Apply Cavalieris principle to use a formula and find the volume of a right or oblique prism
 * Keywords:**
 * Helpful Hints**, rember that you may have to take extra steps to find the base ([|think apothoms],this link can help with many general Q&A)

=**//7.3//**=

//Surface Area and Volume of Pyramids//
1.** Use a formula to find the surface area of a regular pyramid //**Keywords:** [|Pyramid,]// a polyhedron consisting of a base which is a polygon,and three or more lateral faces. //Vertex of a pyramid,// lateral faces of thrangles that share the same, single vertex //Base edge,// each lateral face has one edge in common with the base //Regular pyramid,// a pyramid with base that is a regular polygon and lateral faes are congruent isoceles triangels //Slant height,// length of an altitude of a lateral face of a regualar pyramid. Surface area of a regular pyramid s=l+b or s=1/2lp+b Volume of a pyramid, v=1/3bh
 * //Main Objectives//
 * 2.**Define and use a formula for the volume of a pyrmid.
 * //Formulas//**
 * Example**, a right triangle with a height of 2 and a base of 2, find the volume, V=BH, V=2*2=4^3

//Surface Area and Volume of Cylinders//
//[|Cylinder],// a solid that has a circular region and its translater image on a parallel plane with a lateral surface connection the circles //Axis,// segment joining the centers of the two bases //Formulas//** Surface area for a right cylinder, //s=l+2b or s=2(pi)rh+w(pi)r^2// Volume of a cylinder, //v=bh or v=(pi)r^2h// =168(pi)lateral area. Now the base area. (pi)12^2= 144(pi) surface area= 168(pi)+2(144(pi))=456(pi)
 * //Main Obejectives//**
 * 1.** Use a formula for the surface area of a right cylinder
 * 2.**Use a formula for the volume of a cylinder.
 * Keywords:**
 * [[image:face_tube.jpg link="http://www.flickr.com/photos/s2art/20768675/"]]
 * Example**, a cylinder, r=12 height is 7, find the SA. 2(pi)12*7

Surface Area and Volume of Cones Main Objectives// 1.** Use a formula to find the surface area of a cone Keywords:** Cone, thre dimensional shape figure that has a circular base and a curved lateral surface Surface area of a right cone s=l+b or s=(pi)rl +(p)r^2 Volume of a cone, v=1/3bh or v=1/3(pi)r^2h however it often isnt that easy. Usally you'll have to find the lateral area and the base first.
 * //7.5
 * 2.**Use a formula to find the volume of a cone.
 * [[image:conesbaby.jpg link="http://flickr.com/photos/hamwithcam/sets/579918/with/25524619/"]]
 * Example**, surface area, lets say you have a lateral side area of 50 and a base of 50 all that would need to be done is add them,(100^2)

Surface Area and Volume of Spheres Main Objectives// 1.** Use a formula for the surface area of a [|sphere] (this link gives some general formulas) //Sphere,// the set of all points in space that are the same distance from a given point known as the scether of the sphere. Formulas,** Surface area of a sphere, //s = 4(pi)r^2// Volume of a sphere//, v=4/3(pi)r^3// 1.) If theres a right triangle with 10 cm height and a base of 5 cm V=10*5 V=50^3 2.) If theres a right triangle with 10 cm height and a base of 5 cm S=10*20+2*5 S=210^2 3.) Theres a pyramid with a slant height of 10 and a base of 5 and height of 15 V=1/3*5*15 V=25 4.) surface area of a pyramid S=1/2*10*20+5 S=105 5.) Cylinder with radius of 5 and height of 10 V=p5^2*10 V=785.39 6.) Surface area of a right cylinder S=2p*5*10+2p*5^2 S=471.23 7.)Cone that has a radius of 7 and a height of 15 and slant height of 11 V=1/3p*7^2*15 V=769.69 8.) surface area of a cone S=p*7*11+p*7^2 S=395.84 9.)Sphere with a radius of 50 V=4/3p*50^3 V=523598.77 10.) Surface area S=4p*50^2 S=31415.92
 * //7.6
 * 2.** Use the formula for the volume ofa sphere
 * Keywords:**
 * [[image:bigolsphereballs.jpg link="http://www.flickr.com/photos/tonivanstraaten/362463585/"]]
 * Example**, first take the radius, it should be given, and plug it into the formula 4(pi)r^2 so lets say the radius was 2 it would be 4(pi)2^1 which turns out to be approx.50.27