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 * Ch 7.1 CH 9 __Cr Br 5 25__**

You can try your grasp of surface area and volume with this activity-[|clickhere BC]
 * __Surface Area and Volume__**
 * Explore ratios of surface area to volume.
 * Develope the concepts of maximizing volume and minimizing surface area.
 * __A right rectangular prism__
 * Surface area=2length*width+2Width*height+2length*height
 * Volume=length*width*height
 * __Cube__
 * Surface area=6sides^2
 * Volume=side^2
 * __Example__
 * You are going to build a column. You want the column to be a square prism, what are the possible lengths and dimensions? Fill in the table for the provided lengths.
 * **Lengths** || **SA=2lw+2lh+2wh** || **Volume=lwh** || **Ratio of SA/V** ||
 * 3 ||  ||   ||   ||
 * 6 ||  ||   ||   ||
 * 15 ||  ||   ||   ||



__**CH 7.2 Surface Area and Volume of Prisms**__


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

__Altitude:__ A segment that has endpoints in the planes containing the bases and that is perpendicular to both planes. __Height:__ The length of an altitude.


 * Surface Area of a right prism:** SA=Lateral area=2Base area or SA=Height*Perimeter+2Base
 * Cavalierie's Principals:** 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.
 * Volume of a prism:** V=BH

Find the Surfacs Area of a right prism that is rectangular and has lateral area 25, base area 16, a perimeter of 10 and height of 19. Now find the volume.



A nifty site that calculates everthying for a right prism. http://images.google.com/imgres?imgurl=http://www.1728.com/prism.gif&imgrefurl=http://www.1728.com/volprism.htm&h=380&w=380&sz=6&hl=en&start=21&tbnid=nIldtmcfgtMn8M:&tbnh=123&tbnw=123&prev=/images%3Fq%3DA%2Bright%2Bprism%26start%3D20%26gbv%3D2%26ndsp%3D20%26svnum%3D10%26hl%3Den%26sa%3DN

__**CH 7.3 Surface Area and Volume of Pyramids**__


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

__Pyramid:__ A poly hedron consisting of a base, and three or more lateral faces. __Base:__ A polygon. __Lateral Faces:__ Triangles that share a single vertex. __Vertex of the Pyramid:__ The shared vertex of the lateral faces. __Base Edge:__ The shared edge of the base and a lateral face. __Lateral Edge:__ The intersection of two lateral faces. __Altitude:__ The perpendicular segment from the the vertex to the plane of the base. __Height:__ The length of the altitude. __Regular Pyramid:__ A pyramid whose base is a regular polygon and whose lateral faces are congruent isosceles triangles. __Slant Height:__ The length of an altitude of a lateral face of a regular pyramid.

SA=Lateral Area+Base Area or SA=1/2Slant Height*Base Perimeter+Base Area
 * Surface Area of a regular Pyramid**

V=1/3Base Area*Height
 * Volume of a Pyramid**

Practice:
 * 1) If a painter is painting a sculpture that is in the shape of regular triangular pyramidthat has a lateral area of 15in. and a base area of 12in. how much area must he cover with paint?
 * 2) You are trying to fill a pyramid shaped box with a base area of 6ft. and a height of 12ft. What is the volume?




 * __CH 7.4 Surface Area and Volume of Cylinders__**


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

__Cylinder:__ A solid that consists of a circular region and its translated image on a parallel plane, with a lateral surface connecting the circles. __Altitude:__ A segment that has endpoints in the planes containing the bases and is perpendicular to both planes. __Height:__ The length of the altitude. __Axis:__ The segment joining the centers of the two bases. __Right Cylinder:__ The axis of the cylinder is perpendicular to the bases. __Oblique Cylinder:__ Axis not perpendicular to the bases.

SA=Lateral Area+2Base Area or SA=2πRadius*Height+2πRadius*Height²
 * Surface Area of a Right Cylinder**

V=Base Area*Height or V=πRadius²Height
 * Volume of a Cylinder**


 * 1) If a can has a radius of 3 and height of 13 what is the volume and the surface area?
 * 2) You are trying tofill a circular vat with a base area of 25ft. a lateral area of 70ft and a height of 36ft. What is the volume of the vat?



__**CH 7.5 Surface Area and Volume of Cones**__


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

__Cone:__ A 3D 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.

SA=Lateral Area+Base area or SA=πRadius*Slant Height
 * Surface Area of a Right Cone**

V=1/3Base Area*Height or V=1/3πRadius²Height
 * Volume of a Cone**


 * 1) You are trying to pick the size of ice cream cone you want, one has a base area of 3in. and a height of 7in. the other has a base area of 5in. and a height of 4in. Which has a bigger volume?




 * __Ch 7.6 Surface Area and Volume of Spheres__**


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

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

V=4/3πRadius²
 * Volume of a Sphere**

SA=4πRadius²
 * Surface Area of a Sphere**



All definitions taken from __Geometry__ by Rinehart and Winston.


 * 1) If the height of a rectangular prism is 5in, the length 7in, and the width is 4in. than the volume would be... L*W*H V=5*7*4 V=140in.
 * 2) The surfae area of the above prism is... SA=2Length*Height+2*Length*Width+2*Height*Width SA=2*5*7+2*5*4+2*7*4 SA=166in.
 * 3) A pyramid has a lateral area of 25cm a height of 28cm and a base area of 40cm, what is the surface area? SA=Lateral Area+Base Area SA=25+40 SA=65cm.
 * 4) The volume of the pyramid would be? V=1/3BA*H V=1/340*28 V=373cm.
 * 5) The height of a cylinder is 7in. the base area is 4in. and the lateral area is 12in, what is the volume? V=BA*H V=4*7 V= 28in.
 * 6) What would the surface area of the cylinder be? SA=Lateral Area+2Base Area SA=12+2*4 SA=20in
 * 7) The volume of a cone with a lateral area of 25, a height of 12 and a base area of 34 would be? V=1/3 Base Area*Height V=1/3*34*12 V=136
 * 8) And the surface area of the cone would be? SA=lateral Area+Base area SA=25+34 SA=59
 * 9) What is the volume of a sphere with a radius of 4? V=4/3πRaduis² V=4/3π4² V=67
 * 10) The surface area of the sphere would be? SA=4πRadius² SA=4*π*4² SA=201