huflea

hule517 to chapter 9
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objectives -explore ratios of surface area to volume -develop the concepts of maximizing volume and minimizing surface area

surface area and volume formulas of a cube S= 6s^2 V= s^3 ( S=surface area, V=volume, s=side) example

3X3X3 s=3 V=3^3 S= 6(3^2) surface area and volume formulas for a rectangular prism S=2lw+2wh+2lh V=lwh lenght= 7width=4 height=5 V= (7)(4)(5)=140 S=(2)(7)(4)+(2)(4)(5)+(2)(7)(5) S=56+20+70 S=146 heres a helpful site to help you better understand volume of a cube and rectangular http://www.cimt.plymouth.ac.uk/projects/mepres/book7/bk7i22/bk7_22i2.htm

=__**~*~7.2~*~**__= objectives -use a formula for finding the surface area of a right prism -use a formula finding the volume fo a right prism -use cavalieri's principle to make a formula for the volume of a right or oblique prism

words to know: altititude-the line through the vertex of a figure perpendicular to the base. height- how tall a figure is, the figures tallness. ( [|www.dictionary.com] ) just type in the word you need to know! example of altitude and height. the height or altitude of mount Kilimanjaro is 15,000 feet.

surface area of a right prism S= L+2B or S= hp+2B

Cavalieri's principle if 2 solids have equal heights and the cross sections formed by every plane parallel to the bases of both solids have equal areas, then the 2 solids have equal volumes. example. ( http://www.flickr.com/photos/olr/42675183/ )

volume of a prism V-BH example of a prism

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objectives -use a formula for the surface area of a regular pyramid -use a formula for the volume of a pyramid

words to know: pyramid-a solid having a polygonal base, and triangular sides that meet in a point. example... base- the line or surface forming the part of a figure that is most nearly horizontal or on which it is supposed to stand. lateral faces- triangles that share one vertex vertex of the pyramid- the single place where all the triangles share come to a point called the vertex. base edge- every lateral face has one side (edge) in common with the base called the base edge. lateral edge- the crossing of 2 lateral faces is called a lateral edge altititude-the line through the vertex of a figure perpendicular to the base. height- how tall a figure is, the figures tallness. pyramid-a pyramid whose base is a regular polygon and whose altitude intersects the plane of its base at the center of the base. slant height- the height or altitude of one of the pyramids lateral faces ( [|www.dictionary.com] )

surface area of a regular polygon s=L+B or S= (1/2)lp+B

volume of a pyramid V= (1/3)Bh base= 20X20 B=400 h=50 V=(1/3)(400)(50) V=6666.66667

=__**~*~7.4~*~**__= objectives -use a formula for the surface area of aright cylinder -use a formula for the volume of a cylinder.

words to know... cylinder-solid bounded by two parallel planes and generated by a straight line moving parallel to the given planes and tracing a curve bounded by the planes and lying in a plane perpendicular or oblique to the given planes.

lateral surface- connects both of the circles bases- are the faces formed by the circular region and its translated image. altititude-the line through the vertex of a figure perpendicular to the base. height- how tall a figure is, the figures tallness. oblique cylinder- axis of the cylinder is NOT perpindicular to the bases axis-line segment joining hte centers of hte 2 bases right cylinder- axis of hte cylinder is perpenidcular to the bases

surface area of a right cylinder S=L+2B or S=2(pi)rh+2(pi)r^2

Volume of a cylinder... V=Bh or V= (pi)r^2h

heres a site to help you with surface area and volume of a cylinder http://id.mind.net/~zona/mmts/geometrySection/surfaceAreasAndVolumes/areaVolumeCylinder1.html

=__**~*~7.5~*~**__=

objectives -use the formula of the surface are of a cone -use the formula for the volume of a cone

words to know... cone- a 3 dimensional shape that has a circular base and a curved lateral surface that connects the base to a single point not in the plane of hte base, called a vertex. base- the circular part of the cone lateral surface- connects bas to vertex vertex- the point of the cone where the lateral surface meets at one point altititude-the line through the vertex of a figure perpendicular to the base. height- how tall a figure is, the figures tallness. right cone- altitude of a cone interesects the base of the cone at its center oblique cone- if the altitude of a cone does not intersect the base of the cone at its center

surface area of of a right cone S= L+B or S= (pi)rl+(pi)r^2 heres a website to help you better understand surface area of a cone http://www.uwm.edu/~ericskey/TANOTES/Geometry/node15.html

volume of a cone V= (1/3)Bh or V= (1/3)(pi)r^2h

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objectives -use the formula for the surface area of a sphere -use the formula for the volume of a sphere

words to know.. sphere-generated by the revolution of a semicircle about its diameter; a round body whose surface is at all points equidistant from the center.

annulus- is the ring shaped figure.

volume of a sphere V= (4/3)(pi)r^3

surface area of a sphere S=4(pi)r^2 here a site to help you more with volume and surface area of a sphere http://www.gomath.com/algebra/sphere.php

other websites all pictures are from( [|www.flickr.com] ) and some from ( [|www.google.com] ) definitions are from ( [|www.dictionary.com] )

=__**~*~10 examples!!!~*~**__=

1) volume of triangular prism V=BH B=6 and H=10 V= (6)(10) V=60 2)surface area of a triangular prism S= L + 2B or S=hp +2B L= 300 B= 20 h= 50 S= 300 + 2(20) S= 340

3) volume of a pyramid V= (1/3)Bh B= 76 h=100 V= (1/3)(76)(100) V=2333.33

4)surface area of a pyramid S= L + B or S= (1/2)(l)(p) +B L=80 P=20 B=15 S= 80 + 15 S= 95 5)volume of a cylinder V=Bh or V= (pi)r^2h B= 12 h=24 (12)(24)=288 6)surface area of a cylinder S= L + 2B or 2(pi)rh+2(pi)r^2 L=80 B=20 S= (80)(20) S=1600 7)volume of a cone V= (1/3)Bh or V= (1/3)(pi)r^2h B=76 h=98 V= (1/3)(76)(98)=2482.667 8)surface area of a cone S= L+B or S= (pi)rl + (pi)r^2 L=54 B=31 S=54+31=85 9)volume of a sphere V=(4/3)(pi)r^3 r=12 V=(4/3)(pi)12^3 V=7238.229 10)surfacearea of a sphere S=4(pi)r^2 R=8 S=4(pi)(8^2) S=804.25