shilou

shlo326 //chaptere 9 link


 * __[[image:cube_in_the_city.gif]]Chapter 7__**//

7.1
This site is good for lots of stuff =[|**http://www.mathleague.com/help/geometry/geometry.htm**]= =Objectives:= 1.Explore ratios of surface area to volume. 2.Develop the concepts of maximizing volume and minimizing surface area.

Surface Area and Volume Formulas Of a right rectangular prism [|] Example The apple store is figuring out boxes for their ipods. They want the same volume and the least amount of surface area. Both boxes have a volume of of 160 cubic centimeters. The surface area of box A is 2(8)(5)+2(4)(5)+2(4)(8)=184 square centimeters. The surface area of box B is 2(10)(8)+2(2)(8)+(2)(10)=232 square centimeters. Apple is going to pick box A because it will cost them less for packaging.
 * The surface area (S)
 * The Volume (V)
 * The Lenght (L)
 * The Width (W)
 * The Height (H)
 * S=2LW+2WH+2LH and V=LWH
 * The surface area (S)
 * The Volume (V)
 * The Sides (s)
 * S=6s² and V=s³

7.2
1. Define and use a formula for finding the surface area of a right prism. 2. Define and use a formula for finding the volume of a right prism. 3. Use Cavalieri's Principle to develope a formula for the volumeof a right or oblique prism.
 * Objectives:**


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

Surface Area of a Right Prism Example 1: The area of each base is: B=1/2(2)(21)=21 The perimeter of each base is: P=10+21+17=48 so the lateral area is: L=HP=30(48)=1440 Therefore, the surface area is S=L+2B=1440+2(21)=1440+42=1482
 * Surface Area (S)
 * Lateral Area (L)
 * Base Area (B)
 * Perimeter (P)
 * Height (H)
 * S=L+2B or S=HP+2B

Volume of Right Prisms: Example 2: The volume of fish tank at right, in gallons is found by using the volume formula. BOX=10x7x5 V=BH=LWH=(10)(5)(7)=350 To approximate the volume in gallons, divide by 0.134. V=350÷0.134= about 2,611 gallons
 * Length (L) [[image:rd_cube_NYC.jpg align="right"]]
 * Width (W)
 * Height (H)
 * Volume (V)
 * Base (B)
 * V=BH

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.

Volume of a prism: The volume V, of a prism with height,H, and base area B is V=BH

7.3
1.Define and use a formula for the surface area of a regular pyramid. 2.Define and use a formula for the volume of a pyramid. http://www.321know.com/geo79_x6.htm
 * Objectives:**
 * Pyramid:** A polyhedron consisting of a base, and three or more lateral faces.[[image:3857282284.jpg align="right"]]
 * Base:** The polygonal face that is opposite the vertex.
 * Lateral Faces:** The faces of a prism or pyramid that are not bases.
 * Base Edge:** An edge that is part of the base of a pyramid, each lateral face has one edge in common with the base.
 * Lateral Edge:** The intersection of two lateral faces of a polyhedron.
 * Altitude:** A segment from the vertex perpendicular to the line containing the opposite side.
 * Height:** The length of an altitude of a polygon.
 * Regualr Pyramid:** A pyramid whose base is a regular polygon and whose lateral faces are congruent isosceles triangels.
 * Slant Height:** In a regular pyramid, the length of an altitude of a lateral face.

Example: Find the surface area of a regular square pyramid. The surface area is all the lateral sides plus the base. S=L+B S=4(1/2SL)+S² or S=1/2L(4s)+s²

Surface Area of a Regular Pyramid The surface area,S, of a regular puramid with lateral area,L, base area,B, perimeter of the base,P, and slant height,H, S=L+B Or S=1/2HP+B

Volume of a Pyramid The,V, of a pyramid with height,H, and base area,B, V=1/3BH

7.4
1. Define and use a formula for the surface area of a right cylinder. 2. Define and use a formula for the volume of a cylinder. http://www.mathleague.com/help/geometry/3space.htm#cone with a **lateral surface** connecting the circles. perpendicular to both planes. its an **obique cylinder. __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 or S=2±RH+2±R² The volume, V, of a cylinder with radius, R, height, H, and base area, B, is V=BH or V=3.14R²H
 * //Objectives://**
 * Cylinder-** A cylinder is a solid that consists of a circular region and is translated image on a parallel plane,
 * Bases-** The faces formed by the circular region and its translated image are called the bases of the cylinder.
 * Altitude-** An altitude of a cylinder is a segment that has endpoints in the planes containing the bases and is
 * Height-** The heightof a cylinder is the length of an altitude.
 * Axis-** The axis of a cylinder is the segment joining the centers of the two bases
 * Right cylinder-** If the axis of a cylinder is perpendicular to the bases, then the cylinder is a right cylinder, if not,
 * __Volume of a cylinder.__**

7.5[[image:209199808_3727bfa87f_m.jpg align="right"]]
1. Define and use the formula for the surface area of a cone. 2. Define and use the formula for the volume of a cone. D|http://www.mathleague.com/help/geometry/3space.htm#cone base to a single point not in the plane of the base, called the **vertex. Altitude-** The altitude of a cone is the perpendicular segment from the vertex to the plane of the base. if not, it is an **oblique cone.** The surface area, S, of a right cone with lateral area, L, base of area, B, radius, R, and slant height, L, is S=L+B or S=3.14*RL+3.14*R² The volume, V, of a cone with radius, R, height, H, and base area, B, is V=1/3BH or V=1/3*3.14*R²H
 * //Objectives://**
 * Cone-** A cone is a 3-dimensional figure that consists of a circular **base** and a curved **lateral surface** that connects the
 * Height-** The height of the cone is the length of the altitude.
 * Right cone-** If the altitude of a cone intersects the base of the cone at its center, the cone is a right cone,
 * __Surface area of a right cone.__**
 * __Volume of a cone.__**

7.6
1. Define and use the formula for the surface area of a sphere. 2. Define and use the formula for the volume of a sphere. http://www.mathleague.com/help/geometry/area.htm#areaofacircle as the center of the sphere. in the cylinder are both equal to 525(3.14) square units. The volume, V, of a sphere with radius, R, is V=4/3±R³
 * //Objectives://**
 * Sphere-** A sphere is the set of all points in space that are the same distance, R, from a given point known
 * Annulus-** You can prove that the two red cross sections, the circular region in the sphere and the annulus
 * __Volume of a sphere.__**

Exemple: A workout ball has a radious of 27 inches when fully inflated. Approximentlyhow many cubic inches of air can it hold? V=4/3*3.14r³ =4/3*3.14(27)³ =4/3(19638)3.14 =26,244 cubic inches approximetly 82,488 cubic inches

Chapter 7 Formulas:
1.Volume of a triangle: if its height is 4 base area 40 base perimeter is 28 so S= hp+2B so S=(4)(28)+2(40) put that into the your calculator and it gives you the surface area. 2. Volume of a triangular prism: V=Bh so V=(40)(4) = 160 3. Volume of a pyramid: V=1/3Bh so the base is 9 and the height is 3, V=1/3(9)(3) = 9 4. Surface area of a pyramid:SA=1/2lp+B the slant height is 4 width and length are 3 and the Base is 9, SA=1/2(4)(12)+9 = 33 5. Volume of a cylinder: V=πr^2h if the radius is 10 and the height is 5 V=π(100)(5) = 500π 6. Surface area of a cylinder: SA=2πrh+2πr^2 if the radius is 10 and the height is 5 SA=2π(10)(5)+2π100 = 300π 7. Volume of a cone: V=1/3Bh if the base is 30π and the height is 4 V=1/3(30π)(4) = 40π 8. Surface area of a cone: SA=πrl+πr^2 if the radius is 4 and the slant height is 2 SA=π(4)(2) + π(16) = 24π 9. Volume of a sphere: V=4/3πr^3 if the diameter is 18 V=4/3π(9)^3 = 963.999997π 10. Surface area of a sphere: SA=4πr^2 if the radius is 9 SA=4π(81)= 324π