habada

haad207 chapter 9 link
= =

=__7.1 What we are trying to do in this chapter are:__= 1. Explore ratios of surface are to volume. 2. Develope the concepts of maximizing volume and minimizing surface area. = = S** **2lw + 2wh + 2lh** is the surface area of a rectangular prism and the volume is **v =** **lwh** An example of a rectangular prism could be a cereal box!
 * **SURFACE AREA-** is the total area of all the exposed surfaces of the object.
 * **VOLUME-** is the number of nonoverlapping unit cubes that will exactly fill the interior of a figure.
 * FORMULAS FOR THE SURFACE AND THE VOLUME OF A CUBE AND A RECTANGULAR PRISM!!
 * S** **6s squared** is the surface area of a cube and the volume is **v = S CUBED**

=__7.2 What we are trying to do in this chapter are:__=

1. Define and use a formula for finding the surface area and volume of a right prism. 2.Use cavalieri's principle to develope a formula for the volume of a right oblique prism.


 * [[image:436277174_556043ad69_m.jpg link="http://www.flickr.com/photos/nyah74/436277174/"]]


 * ALTITUDE**- is a segment that has endpoints in the planes containing the bases and that is perpendicular to both planes.
 * HEIGHT-** Is the length of an altitude.

= = S =L + 2B OR S hp + 2B is for the surface area and the volume is V= Bh
 * FORMULAS FOR SURFACE AREA AND VOLUME OF A RIGHT PRISM!!**

__CAVALIERI'S PRICIPLE__ 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 WHAT WE ARE TRYING TO DO IN THIS CHAPTER ARE:__= = = 1. Define and use a formula for the surface area abd volume of a regular pyramid.


 * PYRAMID-** Polyhedron that has a base
 * BASE-** A polygon with 3 or more lateral faces
 * LATERAL FACE-** Triangles that share a single vertex
 * VERTEX OF A PYRAMID-** The single vertex of the lateral face
 * BASE EDGE-** Lateral faces taht have one edge in common with the base
 * LATERAL EDGE-** Intersection of two lateral faces
 * ALTITUDE-** Perpendicular segment from the vertex to the plane of the base
 * SLANT HEIGHT-** Length of an altitude of a lateral face of a regular pyramid


 * FORMULAS FOR THE SURFACE AREA AND THE VOLUME OF A PYRAMID!!**


 * S L+B OR S 1/2 x L x P + B IS THE SURFACE AREA AND THE VOLUME IS V = 1/3B x h**

=**__7.4 WHAT WE ARE TRYING TO DO IN THIS CHAPTER ARE:__**=

1. Use a formula for the surface area of a right cylinder 2.Use a formula for the volume of a cylinder.


 * CYLINDER-** IS A SOLID THAT CONSISTS OF A CIRCULAR REGION AND ITS TRANSLATED IMAGE ON A PARALLEL PLANE
 * LATERAL SURFACE-** CURVED SURFACE OF A CYLINDER
 * BASES-** THE FACES FORMED BY THE CIRCULAR REGION AND ITS TRANSLATED IMAGE
 * ALTITUDE-** A SEGMENT THAT HAS ENDPOINTS IN THE PLANES CONTAINING BASES AND PERPENDICULAR TO BOTH PLANES
 * HEIGHT-** LENGTH OF THE ALTITUDE
 * AXIS-** IS THE SEGMENT JOINING THE CENTERS OF THE TWO BASES
 * RIGHT CYLINDER AND A OBLIQUE CYLINDER-** IF THE AXIS OF THE CYLINDER IS PERPENDICULAR TO THE BASES IT IS A RIGHT CYLINDER, IF NOT IT IS OBLIQUE


 * FORMULAS FOR SURFACE AREA AND THE VOLUME OF CYLINDERS!!**

S L + 2 x b OR S 2PIE x R x H + 2PIE x r SQUARED IS THE SURFACE AREA AND THE VOLUME IS Vb x h OR V PIE x r SQUARED x h =**__LESSON 7.5 WHAT WE ARE TRYING TO DO IN THIS CHAPTER ARE:__**= = = = = =1.Define and use the formula for the surface area of a cone= =2. Define and use the formula for the volune of a cone= = =


 * [[image:at_night.jpg link="http://www.flickr.com/photos/limonada/4288334/"]]

CONE**- Is the three dimentional figure that consists of a cicular base and a curved lateral base that connects the base to a single point not in the plane of the base
 * BASE**- Is the bottom of the cone
 * LATERAL SURFACE**- The curved surface of the cone
 * ALTITUDE**- Is the perpendicular segment from the vertex to the plane of the base
 * HEIGHT**- Is the length of the altitude
 * RIGHT CONE**- If the altitude of a cone intersects the base of a cone at its center then it is a right cone if **NOT** then it is an **OBLIQUE CONE**

= =
 * 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) however it often isnt that easy. Usally you'll have to find the lateral area and the base first

=**LESSON 7.6 WHAT WE ARE TRYING TO DO IN THIS CHAPTER ARE:**=

1. Define and use the formula for the surface area of a sphere 2. Define and use the formula for the volume of a sphereA spere is the set of all points in the space that are the same distance, r, from a given point known as the center of the sphere.


 * Formulas FOR THE SURFACE AREA AND THE VOLUME OF A SPHERE!!**


 * S = 4(pi)r^2** IS THE SURFACE AREA AND THE VOLUME IS //**v4/3(pi)r^3**//

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
 * Example**

1. the volume of a triangular prism is: v=bh the V stands for volume and the B is for the base and the H is for the height. so if the height of the prism is 6 and the base is 3 then you would just multiply the base and the height and that would give u approx 18. 2. the surface area for a triangular prism is: S = hp+ 2B S is for the surface area H is for the height P is for the perimeter and the B is for the base. if you have the same prism as you did in problem #1 and the perimeter is 12 because there is 4 bases then first you multiply the height and the perimeter and that is approx 72 and then u multiply the base times 2 and that is approx 6 and you add those two numbers together 72+6 and that is approx 78 3.the volume of a regular pyramid is: V = 1/3Bh so if the base was 4 and the height is 6 then you multiply 6*4 and that is approx 24 then you multiply by .33 which is the same as 1/3 and that is approx 7.92 4. the surface area of a regular pyramid is: S = 1/2lp + B the L stands for lateral area and the P stands for perimeter and the B stands for the base. if you use the pyramid from #3 then the perimeter is 16 and the lateral face is 12 and the base is 4 then you would multiply lateral area andd the perimeter 12*16 and that is approx 192 then you add that to the base and that is approx 196 and then you multiply that by .5 which is the same as 1/2 abd that is approx 98 5. the volume of a cylinder is: V = pieRsquaredH R stands for the radius and the H stands for the height. so if the radius is 3 and the height is 6 then you go 3.14 which is pie times the radius squared which is approx 28.27 and then you would take that number and multiply that by the height and that is approx 169.62 6. the surface area of a cylinder is: S = 2pieRH + 2pieR squared if you have the same numbers as problem 5 then you would go 2 * pie * the radius * the height and that is approx 113.09 and then you add that number to 2 pie * the radius and that is approx 358.12