mucjos


 * mujo64 chapter 9

7.1 =** //Surface area and Volume//

Objectives at hand:
 * To explore ratios of surface area to vloume.
 * Develop the concepts of increasing Volume and decreasing surface area.

The surface area of an object is the total area of all the exposed surfaces of the object. The volume of a solid object is the number of nonoverlapping unit cubes that will exactly fill the interior of the figure.

//__Surface Area Formulas__// The surface area, S and the volume V of a right rectangular prism with length, width w, and height h are S=2lw +2wh +2lh and V= lwh

The surface area, S, and volume V of a cube with sides s are S= 6s2 and V= s3

Surface Area and Volume of Prisms

Objectives:
 * Define and use a formula for finding the surfae area of a right prism.
 * Define and use a formula for finding the volume of a right prism.
 * Use Cavalieri's Principle for the volume of a right or oblique prism.

Words to know: Altitude- of a prism is a segment that has endpoints in the planes containing the bases and that is perpendicular to both planes. Height- of a prism is the length of an altitude. Cavaleri's Principle- If 2 soilids equal length and the cross sections formed by every plave parallel the bases of both soilids have equal area, then 2 solids, have equal volumes. http://flickr.com/photos/42503982@N00/89091035/in/photostream/

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 surface 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 http://flickr.com/photos/ohjoy1/341531941/
 * 7-3

7.4 Surface area/ volume of cylinders 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 http://flickr.com/photos/jaybee/36251631/
 * define and use a formula for the surface area of a right cylinder
 * define and use formula for the volume of a cylinder

volume and surface area of a right cone

http://flickr.com/photos/hamwithcam/25592321/