kisjos

7-1**
 * kijo61 chapter 9
 * Objectives Objectives[[image:https://whites-geometry-wiki.wikispaces.com/i/c.gif width="8" height="8"]]**
 * Explore ratios of surface area to volume *
 * Develop the concept of maximizing volume and minimizing surface area
 * Formulas for a cube**
 * V = lwh


 * SA = 2lw + 2wh + 2lh

Example
 * size of square || length || width || height || volume ||  ||
 * 1 ||  || 9 || 6.5 || 1 || 58.5 ||   ||
 * 2 ||  || 7 || 4.6 || 2 || 63 ||   ||
 * 3 ||  || 5 || 2.5 || 3 || 37.5 ||   ||
 * x ||  || x^2-11 || x^2-8.5 ||   |||| X x X^2-11 x X^2-8.5 ||

objectives formulas S=L+2B or S=hp + 2B vocabulary altitude- the length of the segment that has endpoints in the planes containing the bases and that perpendicular to both planes hieght- the length of the altitude
 * 7-2**
 * define and use a formula for finding the surface area of a [|right prism]
 * define and use a formula for finding th volume of a right prism
 * use cavalieri's principle to develop a formula for the volume of a right or oblique prism
 * surface area of a right prism- the surface area,S, of a right prismwith lateral area,L,base area B, perimiter p, and height h 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 hev equla areas,then the two solid have equal volume.
 * volume of a prism- the volume, V, of a prism with height h,and base B is V=Bh

surface area of a regular [|pyramid]**- the surface area,S, of a regular pyramid with lateral area L, base area B, perimiter of the base p, and slant height l is S = L + B or 1/2lp + B. volume of a pyramid- the volume,V, of a pyramid with height h and base area B is V = 1/3Bh vocabulary [|pyramid]- a polyhedron consisting of a base and 3 or more lateral faces - polygon of a shape of a prism [|lateral base]- faces of a prism which are not a base [|vertex of a pyramid]-edge that is part of a base base edge-edge that is part of a base [|lateral edge]- intersection of two lateral faces [|regular pyramid]-a pyramid whos base is a regular polygon [|**slant heght**]- in a regular polygon the length f an altitude of a lateral face surface area of a regular pyramid- the surface area, s f a regular pyramid with lateral ae, l base area B permiter of the base p, and slant height l is S=L+B or S=1/2lp+B Volume of a pyramid- the volume v, of a pyramid with height h and base area B is V=1/3Bh Examples find the surfac area of each regular pyramid with side length s and slant height l given below. the number of sides of th base is given by n. 1. S=8 work it out- SA=2pirh + 2pir^2 L=9 N=3 72pi=2pi3h + 2pi3^2 72pi=6pih + 18pi -18pi -18pi 54pi=6pih devide both sides by 6pi h=9 7-4 objectives [|cylinder]-is a solid that consists of a circular region and its translated image on a parallel plane, with a lateral surface connecting the circles surface area of a right cylinder- the surface area of a right cylinder wih lateral area L, base area B, radius r, and height h, s=l+2b or s=2pirh+2pir^2 Example a penny is a right cylinder wih a diameter of 19.05 millimeters and a thickness of 1.55 millimeters. ignoring the raised design,estimate the urface area of a penny. Solution the radius of penny is half of the diameter or 9.525 millimeters. Use the formula for the surface area of a right cylinder. S=2pirh + 2pir^2, S 2pi(9.525)(1.55) + 2pi(9.525)^2663.46 square millimeters. volume of a cylinder- the volume V, of a cylinder with radius,r height h, and base area B is V=Bh or V=pir^2h find the surface area of a quarter. diameter= 24.26mm thickness 1.75 S= 2pi(12.13^2)(1.75) + 2pi(12.13)^2 S=1057.86mm^2 7-5 surface area of a [|right cone]-the surface area of a right cone with lateral area l,base of area B, radius r, and slant height l is s=l+b or s=**π**rl + **πr^2** volume of a cone- the volume v, of a cone with radius r, height h, and base area B is V=1/3bh or v= 1/3**πr^2h** find the surface area of a cone with height=40, radius=9, slant height=49 s=**π9x49 + π9^2 441π + 81π 522π or 1639.08**
 * 7-3
 * define and use a formula for the surface area of a right cylinder
 * define and use formula for the volume of a cylinder

7-6 [|sphere]- the set of points in space that are equidistant fro a given point known as the center of a sphere [|annulus] - the region between two circles in a plane that have the same center but different radii volume of a sphere- the volume,v, of a sphere with radius r is V=4/3**πr^3** example. V=4/3π(27)^3 V=4/3(19,683)π V= 16,244π cubic feet or 82,488 cubic feet** Surface area of a sphere- the surface area,S, of a sphere with radius r is S = 4πr^2 example. =4π(27)^2 =4(729)π =2916π square ft or 9160.9 square feet** Find the surface area and volume of a softball with the diameter of 3.5 inches SA= S=4πr^2 =4π(1.75)^2 =4(3.0625)π = 12.25π inches squared or 38.465 inches squared V=4/3πr^3 =4/3π(1.75)^3 =4/3(5.36)π =7.14π or 22.44π
 * V=4/3πr^3
 * S=4πr^2

1.volume of a triangular prism V=Bh, V=(7)(5), V=35u^3 2.surface area of a triangular prism 3.volume of a pyramid V=1/3Bh ,base area= 1/2Bh,=1/2(4)(3) B=6 H=8 V=1/3(6)(8) = 16u^3 4.surface area of a pyramid SA=1/2lp + B 1/2(6)(16) + 24=72u^2 5.volume of a cylinder diameter 8 height 10 V=πr^2h π(8)^2(10) 640π or 2009.6u3 6.surface area of a cylinder diameter 6 height 8 SA= 2πrh + 2πr^2 =2π(3)(8) + 2π(3)^2 48π + 18π= 64π or 200.96u2 7.volume of a cone radius 7 height 10 V=1/3πr^2 =1/3π(7)^2 16.17π or 50.77u^3 8.surface area of a cone slant height 15 radius5 SA= πrl + πr^2 =π(5)(15) + π(5)^2 75π + 25π= 100π or 314u^2 9.volume of a sphere radius = 9 V=4/3πr^3 =4/3π(9)^3 36π or 113.04u^3 10.surface area of a sphere radius = 22 SA=4πr^2 =4π(22)^2 1936π or 607.04u^2