chrvin

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 * chvi624 Ch 9 link**

=__CHAPTER 7 Surface Area and Volume of Cube and Rectangular Prism__=

LINK-[|ratio game]
 * Explore ratios of surface area to volume
 * Develop the concepts of maximizing volume and minimizing surface area

VOCABULARY:[[image:cubevince1.jpg link="http://www.shutterstock.com/cat.mhtml?searchterm=rubix+cube"]]

 * None

FORMULAS:[[image:boxvince.jpg width="64" height="64" link="http://www.flickr.com/photos/nate/57948792/"]]

 * Surface Area of a Rectangular Prism
 * S=2lw+2wh+2lh (S-surface area, l-length, w-width, h-height)
 * Volume of a Rectangular Prism
 * V=lwh
 * Surface Area of a Cube
 * S=6s² (s-side)
 * Volume of a Cube
 * V=s³

OBJECTIVES:
Define and use a formula for finding the volume of a right prism LINK- [|surface area of a rectangular prism]
 * Define and use a formula for finding the surface area of a right prism
 * Use Cavalieri's Principle to develop a formula for the volume of a right or oblique prism


 * Height of a Prism [[image:prismvince10000.jpg width="133" height="113" link="http://www.flickr.com/photos/ninjatune/280686783/"]]
 * The length of the altitude
 * Altitude of a Prism
 * A segment that has endpoints in the planes containing the bases and that is perpendicular to both planes.
 * Cavalieri's Principle
 * If 2 solids have equal heights and the cross sections formed by every plane parallel to the base of both solids have equal areas, then the two solids have equal volume.

FORMULAS:
S=hp+2B (S-surface area, h-height, p-perimeter, B-base area)
 * Surface Area of a Right Prism
 * Volume of a Prism
 * V=Bh (V-volume, B-base area, h-height)

OBJECTIVES
LINK- [|volume of a pyramid game]
 * Define and use a formula for the surface area of a regular pyramid [[image:pyramidvince000000000000.jpg width="97" height="100" link="http://www.flickr.com/photos/fotoblitzcolor/410779616/"]]
 * Define and use a formula for the volume of a pyramid

VOCABULARY:

 * Pyramid
 * A polyhedron consisting of a base, which is a polygon, and 3 or more lateral faces.
 * Base
 * The polygonal face that is opposite the vertex.
 * Lateral Faces
 * The faces of a prism or pyramid that are not bases.
 * Vertex of a Pyramid
 * A point where the edges of a figure intersect.
 * Base Edge
 * An edge that is part of the base of a pyramid; Each lateral face has one edge in common.
 * Lateral Edge
 * The intersection of 2 lateral faces.
 * Altitude of a Pyramid
 * A segment from the vertex perpendicular to the plane base.
 * Height
 * The length of the altitude.
 * Regular Pyramid
 * A pyramid whose base is a regular polygon and whose lateral faces are congruent.
 * Slant Height
 * In a regular pyramid, the length of the altitude of a lateral face.

FORMULAS:

 * Surface Area of a Regular Pyramid
 * S=½lp+B (S-surface area, l-slant height, p-perimeter of base, B-base area)
 * Volume of a Pyramid
 * V=1/3Bh (V-volume, B-base area, h-height)

SECTION 4 OBJECTIVES:
LINK- [|VOLUME of CYLINDER]
 * Define and use a formula for the surface area of a right cylinder
 * Define and use a formula for the volume of a cylinder

VOCABULARY:[[image:can0000000vince.jpg width="106" height="90" link="http://www.flickr.com/photos/yerffej9/198436204/"]]

 * Cylinder
 * A solid that consists of a circular region and its translation image on a parallel plane.
 * Lateral Surface
 * Conects the circle.
 * Base
 * Formed by the circular region and its translated image.
 * Altitude
 * A segment that has endpoints in the planes contaning the bases and is perpendicular to both planes.
 * Height
 * The length of an altitud
 * Axis
 * Segment joining the center of the two bases.
 * Right Cylinder
 * The axis of a cylinder is perpendicular to the bases to the bases.
 * Oblique Cylinder
 * The axies are not perpendicular.

FORMULAS:

 * Surface Area of a Right Cylinder- S=L+2B or S= 2*Pi*RH+R^2 (S-surface area, L- lateral area, B- base area, R- radius, H-height)
 * Volume of a Cylinder V=BH or V= Pi*R^2H (V- volume, R- radius, H- height, B- base area)

OBJECTIVES:
LINK- [|VOLUME of CONE GAME]
 * Define and use the formula for the surface area of a cone [[image:cone.jpg width="106" height="97"]]
 * Define and use the formula for the volume of a cone

VOCABULARY:

 * Cone- 3-dementional 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- A circular surface.
 * Lateral Surface- A curved surface.
 * Vertex- connects the base to a single point not in the plane of the base.
 * Altitude- The purpendicular segment from the vertex to the plane of the base.
 * Height- The length of an altitude.
 * Right Cone- The altitude of a cone intersects the base of the cone at its center.
 * Oblique cone- The altitude of the cone doesn't intersect the base of the cone at its center.

FORMULAS:

 * Surface Area of a Right Cone- S=L+B or S=Pi*RL+Pi*R^2 (S- surface area, L- lateral area, B- base area, R- radius, l- slant height)
 * Volume of a Cone- V=1/3Pi*BH or V=1/3Pi*R^2H (B- base area, R- radius, V- volume, H- height)

OBJECTIVES:

 * Define and use the formula for the surface area of a sphere
 * Define and use the formula for the volume of a sphere [[image:sphere.jpg width="64" height="64"]]

VOCABULARY:

 * Sphere- The set of all points in space that are the same distance, r, from a given point known as the center of the sphere.
 * Annulus- A ring shapped figure in a cylinder.

[|Sphere Game]

FORMULAS:

 * Surface Area of a Sphere- S=4Pi*R^2 (S- surface area, R- Radius)
 * Volume of a Sphere- V=4/3Pi*R^3 (V- volume, R- radius)

OTHER FUN GEOMETRY LINKS: [|GAMES], [|FACTS]

Examples:

VOLUME OF A PRISM: V=BWH

the cube above is 3*3*3

to get the volume you would go: B* W* H 3* 3* 3 = 27 units^3 _ SURFACE AREA OF A PRISM:

S=2lw+2wh+2lh

the cube above is 3*3*3

S=2(3*3)+2(3*3)+2(3*3)= 54 units^2

__VOLUME OF A PYRAMID:

V=1/3Bh

the pyramid above has a base of 17, and a height of 300

1/3 B h 1/3(17*300)=1699.99units^3__

_

SURFACE AREA OF A PYRAMID:

S=½lp+B

the pyramid above has a base perimeter of 20, and a slant height of 70.

if the base perimeter is 20, it concludes that each side of the pyramid is 5. then you multiply 5*5=25 25 is the base area.

½lp+B

(1/2)(70*20)+25=725 units^2

VOLUME OF A CYLINDER: V= Pi*R^2H the cylinder above has a radious of 1 and a height of 6

Pi*R^2H 3.14*1^2*6=18.84 units^3

_

SURFACE AREA OF A CYLINDER

S= 2*Pi*RH+R^2

the cylinder above has a radious of 1 and a height of 6

2*Pi*RH+R^2 2*3.14*1*6+1^2=37.68 units^2

___