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7.1 SA and Volume__** Objective: Explore ratios of SA to volume.
 * __ch9 muha313

Objective:Develope the concepts of maximizing Volume and minimizing SA.


 * __SA/ Volume of a right rectangluar prism:__**

2=2lw+2wh+2lh and V=lwh


 * __SA/ volume of a cube:__**

S=6s2 and v=s3


 * __7.2 SA and Volume of Prisms

Objective: Define and use formula for finding SA of a Right prism.

Objective:__**Use Cavalieri's Principle to develop a formula for the V of a Right or Oblique Prism.


 * __Altitude:__** //Endpoint on segment in the planes sontaining the bases and hat is perpendicular to both planes.


 * __Height:__** Length of an altitude.


 * __SA of a Right Prism:__** S=L+2B or S=hp+2B. B is the area of base and L is area of all lateral faces.


 * __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 equan areas, then the two solids have equal volumes.

Example: dimentions: 11x9x8 In order to find the volume of this rectangular prism, we have to use the formula V=bh (V=LWH). So we have to go 11x9, which is 99. Then 99x8 which is 792 //**__7.3 SA and Volume of Pyramid__
 * __Volume of a Prism:__** V=bh. base times height.//

Objective: Define and use formula for the SA and V or a regular pyramid.

__Pyramid:__** A polyhedron consisting of a base.

__Base__: Polygon, with three or more lateral faces. __Lateral faces__: Triangles that share a single vertex. __Vertex of the pyramid__:Lateral faces share this. __Base edge__: Each lateral face has one edge in common with this. Altitude://The altitude of a pyramid is the perpendicular segment from the vertex to the plane of the base. Height: The height of the pyramid is the length of the altitude. //__Lateral edge__: Intersection of two lateral faces is this. Slant height:// The slant height is the length of an altitude of a lateral face of a regular pyramid.

//**SA of a regular Pyramid:** S=L+B or S=1/2lp+B The SA of a regular pyramid with lateral area, base area, perimeter of the base, and slant height.

__**Volume of a Pyramid**__: The volume of a pyramis with height and base area: V= 1/3 Bh.//

Objectives:__//** Define and use a formula for the SA and V of a cylinder.
 * //__7.4 SA amd Volume of Cylinders

//**__Cylinder:__** A solid that cinsists of a circular region an its translated image on a parallel plane. Lateral sirface: Connects the circles. Bases: Faces formed by he circular region and its translated image. Altitude: Segment that has endpoints in th eplanes containing the bases and is perpendicular to both planes. Height: Length of and altitude. Axis: Segment joining the centers of the two bases. Right cylinders: Is the axis of a cylinder is perpendicular to the bases. Oblique: If the cylinder is not perpendicular to the bases.



http://library.thinkquest.org/C006354/cylinder.gif

SA of a Right Cylinder: The SA of a right cylinder with laer area, base area, radius, and height is S=L+2B

Volme of cylinder: The volume or a cylinder with radius, height, and base aea is V=Bh.

ex.

__**7.5 SA and Volume of Cones**__ Objectives://Define and use a formula for the SA and V of a cone.

//Cone: Three-dimensional figure that consists of a circular base and a curved lateral face that connects the base to a single point no in the plan eof the base. Base: curved lateral face. Lateral face: Connects he base to a single point not in the plane of the base. Vertex: Point not in the plane of the base. Altitude: Perpendicular segment from the vertex to the plane of the base. Height: Length of the altitude Right cone: If the altitude of a con intersects the base of the cone at it's center. Oblique cone: If the altitude of a cone doesnt intersect the base of the cone at its center. Slant height for a cone:// When you have a net for a cone, the lateral face creates the area of Pi, This is called the sector. The radius of the sector is the slant height //SA of a Right cone: The SA of a right cone with laer a area, base are, radius, and slant height is: S=L+B

Volume of a Cone: The volume of a cone with radius, height, and base area is:

V= 1/3 BH//

Objectives:__//** Define and use a formula for the SA and V of a sphere.
 * //__7.6 SA and Colume of Sphere

//**__Sphere:__** The set of all points in space hat are the same distance, from a given point known as the center of the sphere.

Volume of a Sphere-The Volume, V, of a sphere whith radius r is: V=4/3(3.14)r^3 //Volume of a Sphere: The volume of a sphere with radius is V=4/3 (3.14)3
 * __Annalus__**://When a plane intersects a sphere or a cylinder, it creates a ring-like cross section called the annalus.

SA of a sphere: The SA of a sphere with radius is S=4(3.14)2

1. Volume of atriangular prizm: 2. SA of triangular prizm 3. Volume of a pyramid. 4. SA of a pyramid 5. Volume of a cylinder 6. SA of cylinder 7. Volume of a cone 8. SA of a cone 9. Volume of a sphere 10. SA of a sphere//