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=joam321 link to ch 9= = = = = =http://en.wikipedia.org/wiki/Volume=

The objectives of 7.1
__**Surface area for right rectangular prisms**__ S=2lw+2lh+2wh for a cube this becomes S=6s²
 * Explore ratios of Surface Area and Volume successfully.
 * Develop the concepts of maximizing Volume and minimizing Surface Area successfully.

__Volume formulas for right rectangular prisms__
V=lwh for a cube it becomes V=s³

__7.2__ //__Surface Area and Volume of Prisms__//
[|surface area of prisms] The objectives of 7.2 Sometimes the height of a prism is call the **altitude.**
 * Define/use a formula for finding the Surface Area of a right prism successfully.
 * Define/use a formular for finding the Volume of a right prism successfully.
 * Use Cavalieri's Principle to develop a formular for the Volume of a right or oblique prism successfully
 * **//Altitude//** - of a prism is a segment that conects the bases of a prism, perpendiculary.
 * ===//Height-// of a prism is the length of an altitude.===

__Surface area of a Right Prism__
[|Prisms]
 * __Volume of a Prism-__** Volume V of a prism with height h and base area B is **V= Bh**
 * __Cavalieri's Principle-__** If two solids both 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.

The objectives of 7.3
 * __[|7.3 Surface Area and Volume of Pyramids]__**
 * Define/use a formula for the surface area of a regular pyramid successfully.
 * Define/use a formular for the volume of a pyramid successfully.

//S= L+B or S= 1/2 lp+B// [|Pyramid] __7.4 Suface Area and Volume of Cylinders__** The objectives of 7.4 are clear:
 * **Pyramid**- A polyhedron consisting of a
 * **base**base (the polygonal face that is opposite the vertex), and three or more
 * **lateral faces**lateral faces (face of a prism/pyramid that is not the base).
 * **Vertex of the Pyramid**Vertex of the Pyramid- The lateral faces that share a single vertex.
 * **Base Edge-**Base Edge- The edge that each lateral face has in common with the base.
 * **Lateral Edge**Lateral Edge- The intersection of two lateral faces.
 * **Altitude-**Altitude- A segment that has endpoints in the planes containing the bases and that is perpendicular to both planes.
 * **Height-**Height- The length of the altitude.
 * **Regular Pyramid-**Regular Pyramid- A pyramid whos base is a regular polygon.
 * **Slant Height-**Slant Height- The length of an altitude of a lateral face of a regular pyramid.
 * __Surface Area of a regular Pyramid__**
 * __Volume of a Pyramid__**
 * V= 1/3Bh
 * Define/use a formula for the Surface Area of a right cylinder successfully.
 * Define/use a formula for the Volume of a cylinder successfully.


 * Cylinder-** A solid that consists of a circular region and its translated image on a parallel plane with a
 * Lateral surface** (surface connecting the bases) connecting the circles.
 * Bases-** The faces formed by the circular region and its translated image.
 * Altitude-** A segment that has endpoints in the planes containing the bases and that is perpendicular to both planes.
 * Height-** The length of the altitude.
 * Axis-** The segment joining the centers of the two bases.
 * Right Cylinder-** If the axis of a cylinder is perpendicular to the bases, then it is this form.
 * Oblique Cylinder-** If the axis of a cylinder is not perpendicular to the bases, then it is this form.

//**__Surface Area of a Right Cylinder__**// The Surface Area SA of a right cylinder with lateral area L, base area B, radius r, and height h is
 * S= L+2B** or
 * S= 2 x pi x r x h +** **2 x pi x r^2**

The Volume V of a cylinder with radius r, height h, and base area B is The objectives of 7.5
 * __The Volume of a Cylinder:__**
 * V= Bh** or **pi x r^2 x h**
 * __7.5 Surface area and Volume of cones__**
 * Define/use the formula for the Surface Area of a cone successfully.
 * Define/use the formula for the Volume of a cone successfully.

Definitions
 * **Cone-** A three-dimensional figure that consists of a circular
 * **base**base (the face formed by its circular region) and a curved
 * **lateral surface**lateral surface (a lateral face) that connects the base to a single point not in the plane of the base,
 * vertex (lateral faces meeting together in the same point).
 * **Altitude-**Altitude- A segment that has endpoints in the planes containing the bases and that is perpendicular to both planes.
 * **Height-**Height- The length of the altitude.
 * **Right Cone-**Right Cone- If the altitude of a cone intersects the base of the cone at its center, the cone is right.
 * **Oblique Cone-**Oblique Cone- If the altitude of a cone does not intersect the base of the cone at its center, the cone is oblique.

The Surface Area (SA) of a right cone with lateral area (L), base of area (B), radius (r), and slant height (l) is **S= L+B** or
 * __Surface Area of a Right Cone__**
 * S= pi x r x l+pi x r^2

__Volume of a Cone__** The Volume (V) of a cone with radius (r), height (h), and base area (B) is V (1/3)Bh or V (1/3) x pi x r^2 x h

__**7.6 The objectives of 7.6**__ = =
 * Define/use the formula for the Surface Area of a sphere successfully.
 * Define/use the formula for the Volume of a sphere successfully.

__Definitions__ [|Sphere] __**Volume of a Sphere**__ The Volume V of a sphere with radius r is V= 4/3pi x r^3 __**The Surface Area of a sphere** SA= 4 x pi x r^2 http://www.ics.uci.edu/~eppstein/junkyard/sphere.html __
 * **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-** The ring-shaped figure within the sphere.
 * 1) surface area of a triangular prism- if its height is 4 base area 40 base perimeter is 28 so S= hp+2B so S=(4)(28)+2(40) put that into the your calculator and it gives you the surface area.
 * 2) volume of a triangular prism- V=Bh so V=(40)(4) = 160
 * 3) volume of a pyramid- V=1/3Bh so the base is 9 and the height is 3, V=1/3(9)(3) = 9
 * 4) surface area of a pyramid- SA=1/2lp+B so the slant height is 4, width and length are 3 and the Base is 9 so SA=1/2(4)(12)+9 = 33
 * 5) volume of a cylinder- V=πr^2h if the radius is 10 and the height is 5 V=π(100)(5) = 500π
 * 6) surface area of a cylinder- SA=2πrh+2πr^2 if the radius is 10 and the height is 5 SA=2π(10)(5)+2π100 = 300π
 * 7) volume of a cone- V=1/3Bh if the base is 30π and the height is 4 V=1/3(30π)(4) = 40π
 * 8) surface area of a cone- SA=πrl+πr^2 if the radius is 4 and the slant height is 2 SA=π(4)(2) + π(16) = 24π
 * 9) volume of a sphere- V=4/3πr^3 if the diameter is 18 V=4/3π(9)^3 = 963.999997π
 * 10) surface area of a sphere- SA=4πr^2 if the radius is 9 SA=4π(81)= 324π