drajac


 * drja227

__7.1 SURFACE AREA & VOLUME__

Objective-** Explore ratios of [|surface area] to volume.
 * Objective-** Develope the concepts of maximizing [|volume] and minimizing surface area.

To get the surface area and volume of a rectangular prism with the [|length], [|width], and [|height], use the following formulas... To get the surface area and volume of a cube with the sides use the following formulas...
 * Surface Area and Volume:**
 * S =2lw + 2wh + 2lh and V lwh**
 * S =6s² and V** **s³**


 * __7.2 SURFACE AREA & VOLUME OF PRISMS__

Objective-** Define and use a formula for finding the surface area of a right prism.
 * Objective-** Define and use a formula for finding the volume of a right prism.
 * Objective-** Use Cavalieri's Principle to develope a formula for the volume of a right or oblique prism.

__**Definitions**__ [|Altitude] [|Height]

The Surface Area of a right prism with lateral area, base area, perimeter, and height is...
 * Surface Area of a Right Prism:**
 * SA=L+2B or SA=hp+2B**

Volume of a Prism: The Volume of a prism with height and base area 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 have equal areas, then the two solids have equal volumes.
 * V= BH


 * __7.3 SURFACE AREA & VOLUME OF PYRAMIDS__

Objective-** Define and use a formula for the surface area of a regular pyramid.
 * Objective-** Define and use a formula for the volume of a pyramid.


 * __Definitions__**
 * Pyramid-** A polyhedron consisting of a base.
 * Base-** Bottom and top of a figure or shape.
 * Lateral Face-** Triangles that share a single vertex.
 * Vertex of the Pyramid-** Single vertex.
 * Base Edge-** Each lateral face has one edge in common with the base.
 * Lateral Edge-** Intersection of two lateral faces.
 * Altitude-** Perpendicular segment from the vertex to the plane of the base.
 * Height-** Length of altitude.
 * Regular Pyramid-** A pyramid whose base is a regular polygon and whose lateral faces are congruent isocesles triangles.
 * Slant Height-** Length of an altitude of a lateral face of a regular pyramid.

The Surface Area of a regular pyramid with lateral area, base area, perimeter of the base, and slant height is...
 * Surface Area of a Regular Pyramid:**

SA=½ lp+B
 * SA=**L+B or


 * [[image:pyrmaid-jd.jpg width="334" height="230" link="http://flickr.com/photos/deestea/123564992/"]] ||

1/3 × [Base Area] × Height

The Surface Area of a Pyramid
1/2 × Perimeter × [Side Length] + [Base Area] The volume of a pyramid with height and base area is...
 * Volume of a Pyramid:
 * V= 1/3Bh**


 * __7.4 SURFACE AREA & VOLUME OF CYLINDERS__

Objectives-** Define and use a formula for the surface area of a right cylinder.
 * Objectives-** Define and use a formula for the volume of a cylinder.


 * __Definitions__**
 * Cylinder-** A solid that consists of a circular region and it's translated image on a parallel line.
 * Lateral Surface-** Connects the circles.
 * Bases-** The faces formed by the circular region and its translated images.
 * Altitude-** A segment that has endpoints in the planes containing the bases and is perpendicular to both planes.
 * Height-** Length of an altitude.
 * Axis-** The segment joining the centers of the two bases.
 * Right Cylinder-** When the axis of a cylinder is perpendicular to the bases.
 * Oblique Cylinder-** a non-right prism or cylinder.

The Surface Area of a right cylinder with lateral area, base area, radius, and height is... S=2πrh + 2πr²** ||
 * Surface Area of a Right Cylinder:**
 * S=L+2B or
 * [[image:cylinder-jd.jpg width="442" height="268" align="center" link="http://flickr.com/photos/wirerabbit/357616830/"]] ||
 * [[image:cylinder-jd.jpg width="442" height="268" align="center" link="http://flickr.com/photos/wirerabbit/357616830/"]] ||

The volume of a cylinder with radius, height, and base area is... V=πr²h**
 * Volume of a Cylinder:**
 * V=Bh or


 * __7.5 SURFACE AREA & VOLUME OF CONES__

Objectives-** Define and use the formula for the surface area of a cone.
 * Objectives-** Define and use the formula for the volume of a cone.


 * __Definitions__**
 * Cone-** Three-dimensional figure with a circular base.
 * Base-** Bottom/Top of a figure or shape.
 * Lateral Surface-** Connects the base to a single point.
 * Altitude-** The perpendicular segment from the vertex to the plane of the base.
 * Height-** Length of the altitude.
 * Right Cone-** Intersection of the base of the cone at the center (90° angle).
 * Oblique Cone-** A non-right cone.
 * Slant Height of a Cone-** Height of slanted area.

The Surface Area of a right cone with lateral area, base of area, radius, and slant height is... S=πrl + πr²** The Volume of a cone with radius, height, and base area is... V=1/3πr²h**
 * Surface Area of a Right Cone:**
 * S=L+B or
 * Volume of a Cone:**
 * V=1/3Bh or

__**7.6 SURFACE AREA & VOLUME OF SPHERES**__


 * Objective-** Define and use the formula for the surface area of a sphere.
 * Objective-** Define and use the formula for the volume of a sphere.


 * __Definitions__**
 * Sphere-** The set of all points in a space that are the same distance from a given point known as the center of the sphere.
 * Annulus-** A ring; the area bounded by two concentric circles

The Volume of a sphere with radius is...
 * Volume of a Sphere:**
 * V= 4/3πr³**

Surface Area of a Sphere: The Surface Area of a sphere with radius is...
 * S= 4πr²

[|* * * *GEOMETRY SHAPE GAMES* * * *]**