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 * brtr57 chapter 9 wiki

Lesson 7.1**

1. Surface Area and Volume Formula: The surface area S, and the volume V, of a right rectangular prism with length l, width w, and height h are: S=2lw+2wh+2lh V=lwh The surface area S, and volume V, of a cube with side s are: S=6s² V=s³



http://www.math.com/tables/geometry/surfareas.htm


 * Lesson 7.2**

1. 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 S=hp+2B 2. 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. 3. Volume of a Prism The volume V, of a prism with height h and base area B is: V=Bh



http://www.teacherschoice.com.au/Maths_Library/Area%20and%20SA/area_9.htm


 * Lesson 7.3**

1. Surface Area of a Regular Pyramid The surface area S, of a regular pyramid with lateral area L, base area B, perimeter of the base p, and slant height l is: S=L+B S=1/2lp+B 2. Volume of a Pyramid The volume V, of a pyramid with height h and base area B is: V=1/3Bh

http://www.mathsisfun.com/geometry/pyramids.html


 * Lesson 7.4**

1. Surface Area of a Right Cylinder The surface area S, of a right cylinder with lateral area L, base area B, radius r, and height h is: S=L+2B S=2//π//rh+2//π//r//²// 2.Volume of a Cylinder The volume V, of a cylinder with radius r, height h, and base area B is: V=Bh V=//πr²h//



http://www.aaamath.com/g79-surface-area-cylinder.html


 * Lesson 7.5**

1.Surface Area of a Right Cone The surface area S, of a right cone with lateral area L, base area B, radius r, and slant height l is: S=L+B S=//πrl+πr²// 2.Volume of a Cone The volume V, of a cone with radius r, height h, and base area B is: V=1/3Bh V=1/3//πr²h//

http://www.webcalc.net/calc/0040_help.php


 * Lesson 7.6**

1. Volume of a Sphere The volume V, of a sphere with radius r is: V=4/3//πr³// 2.Surface Area of a Sphere The surface area S, of a sphere with radius r is: S=4//πr²//



http://library.thinkquest.org/C0110248/geometry/menareasphere.htm

__**Vocabulary**__ __7.1__- None __7.2__- Altitude - A segment that has endpoints in the planes containing the bases and that is perpendicular to both planes. Height - The length of an altitude. __7.3__ - Pyramid - A polyhedron consisting of a base and three or more lateral faces. Base - A polygon. Lateral Face - triangles that share a single vertex. Vertex of the Pyramid - The lateral faces are triangles taht share a single vertex. Base Edge - One edge taht each lateral face has in common with the base. Lateral Edge - The intersection of two lateral faces. Altitude - The perpendicular segment from the vertex to the plane of the base. Height - The length of its altitude. Regular Pyramid - A pyramid whose base is a regular polygon and whose lateral faces are congruent isoseles triangles. Slant Height - The length of an altitude of a lateral face of a regular pyramid. __7.4__ - Cylinder - A solid that consists of a circular region and its translated image on a parallel plane with a lateral surface connecting the circles. Lateral Surface - Connects the circles 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 the bases and is perpendicular to both planes. Height - The length of an altitude. Axis - The segment joining the centers of the two bases. Right Cylinder - If the axis of a cylinder is perpendicular to the bases. Oblique Cylinder - If the axis of a cylinder is not perpendicular to the bases. __7.5__ - Cone - Three-dimensional figure that consists of a circular base and a curved lateral surface that connects the base to a single point not in the plane of the base. Base - Bottom of a cone. Lateral Surface - The side of the cone. Vertex - A single point not in the plane of the base. Altitude - The perpendicular segment from thte vertex to the plane of the base. Height - The length of the altitude. Right Cone - If the altitude intersects the base of the cone at its center. Oblique Cone - If the altitude does not intersect the base of the cone at its center. __7.6__ - Sphere - The set of all points in space taht are the same distance, r, from a given point known as the center of the sphere. Annulus - The ring shaped figure in a cylinder.

http://www.andrews.edu/~calkins/math/webtexts/geom10.htm http://education.yahoo.com/homework_help/math_help/problem_list?id=minigeogt_11_1 http://math2.org/math/geometry/areasvols.htm http://www.math.com/tables/geometry/volumes.htm http://www.science.co.il/Formula.asp
 * Additional Formulas For Learning!**

__#1.Volume of a triangular prism__ Dr. Gyaberry is remodeling his office to be in the shape of a giant glass prism. His practice is in Chinese water therapy and therefore he needs to know how many gallons of water his room can hold. Find the volume of his new room if the measurements are 125x54x8ft. V=Bh=lwh=(125)(54)(8)=54000 ft.
 * Problems to Help you LEARN!**

__#2.Surface area of a triangular prism__ After all of the measurements, Stanley needs to find the surface area of his stainless steel prism so he can know how much silver to buy to coat it in. Here are the measurements: h=4in. p=26in. B=12in. S=hp+2B=(4)(26)+2(12)=104+24=128 S=128in.

__#3.Volume of a pyramid__ Gordy Horn is building a shrine for his black lab that that tragically died by digging a hole that it could not get out of. To fit in his yard he needs the pyramid to have a volume of 16.6 sq. ft. and a base area of 5 sg. ft. What is height does the pyramid have to be? V=1/3Bh 16.6=1/3(5)h 16.6=1.6h 16.6/1.6 h=10

__#4.Surface area of a pyramid__ Shauna Bondwells is in charge of cleaning the glass pyramid call Le Louvre. The architect gave her these measurements: L=45ft., p=180ft., B=2,025 Find the surface area to help Shauna figure out how much soap she needs. S=1/2lp+B S=1/2(45)(180)+2025 S=1/2(10125) S=5062.5

__#5.Volume of a cylinder__ Because of an ice age, there is now a shortage of tomatoes. The Cambell soup company has decided to downsize its cans. If their original can had a height of 6in. and a diameter of 3 in., what would the new cans measurements be if they were to subtract 2 inches from the height and 1 inch from the diameter? What would the new can’s volume be? 6-2=4 inches (height) 3-1=2 inches (diameter) V=//π//r²h V=//π//(12)(4) V=12.56

__#6.Surface area of a cylinder__ The Cambell soup company now needs to know the surface area of the can to determine how big the label has to be. Use the same measurements to determine the surface area. S=2//π//rh+2//π//r² S=2//π//(1)(4)+2//π//1² S=25.1+6.3 S=31.4

__#7.Surface area of a cone__ It is little Debbie's 5th Birthday and she needs to know the surface are of her party hat so she know how much glitter to buy. The diameter of the cirlcle that will used to make the party hat is 12in and the length is 6in. What is the surface area? S=//πrl+πr//² S=//π(6)(6)+π6//² S=113+113 S=226

__#8.Volume of a cone__ Find the volume of the cone with the indicated measurements: d=7in., h=5in. V=1/3//π//r²h V=1/3//π//(3.5²)(5) V=64.14

__#9.Volume of a sphere__ Nancy needs to know how much air to pump into her basketball. What is the volume of her basketball, if it has a radius of 4in.? V=4/3//π//r³ V=4/3//π//4³ V=268 __#10.Surface area of a sphere__ Gobya Strauss is making a pinata that is a perfect sphere with a diameter of 64in. She needs to know the surface area of the pinata to know how much tissue paper to buy. What is the surface area? S=4//π//r² S=4//π//(32²) S=12868