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Math 7.1 Surface Area and Volume.
Objectives- To explore ratios of Surface area to Volume. -Develop the concepts of maximizing volume and minimizing surface area. surface area= S=2//lW+2hW+2lh// Volume= lwh Surface Area=6s^2 Volume= s^3 Find the surface area and volume of a RECTANGULAR prism with a length of-2 a height of-1 and a width of -2. Surface area= 2//lW+2hW+2lh// 2•2•2+2•1•2+2
 * Rectangular prisms**
 * Cubes**
 * ACTIVITY--**

Frst607 Chapter 9 linkFor more of an understanding on surface area and volume click on the link below and you will have to scroll down to the formulas http://argyll.epsb.ca/jreed/math9/strand3/3107.htm

7.2 -Surface Area and Volume of PRISM
==[|][|][[[|http://flickr.co][|]m/photos/22064392@N00/171438541/|]]== vocab--
 * altitude**- a segment that has endpoints in the planes containing the abses and that is perpendicular to both planes.
 * Height**- height of a prism is the length of an altitude.
 * Surface area Of Right Prisms-** S=L+2B or S=hp=2B
 * Volume of Right Prisms-** V=Bh
 * Cavalieris Principle-** If two solids have equal heights and the cross sections formed by every plane parallel to the bases of both solids have the equal areas, then the two solids have equal volumes.

7.3- Surface Area and Volume of Pyramids
pyramid- Is a polyhedron consisting of a BASE(which is a polygon) and there are 3 or more lateral faces. Lateral faces- the triangles that share a single vertex called the Vertex of the pyramid. Base edge- Each lateral face has one edge in common with the base Lateral edge- the intersection of two lateral faces. Altitude- of a pyramid is the perpendicular segment from the vertex to the plane of the base. height- of a pyramid isthe length of its altitude. Regular Pyramid- is a pyramid whose base is a regular polygon and whose lateral faces are congruent isosceles triangles.
 * vocab-**[[image:http://farm1.static.flickr.com/168/432574544_d0e51972e9.jpg?v=0 width="237" height="159" link="http://flickr.com/photos/mattosensei/432574544/"]]
 * For a fun way to learn more clearly on the area and volume on pyramids this is a GREAT website to learn from--- http://www.mathsisfun.com/geometry/pyramids.html**

//7.4 Surface Area and Volume of Cylinders//
Vocab- Cylinder- is a solid that consists of a circular region and its translated image on a parallel plane, with a LATERAL SURFACE connecting the circles. Bases- The faces formed by the circualr region and its translated image Altitude- Of a cylinder is a segment that has endpoints in the planes containing the bases and is perpendicular to both planes. Height- of a cylinder is the length of an altitude Axis- of a cylinder is the segment joining the centers of the two bases. Right Cylinder- if the axis of the cylinder is perpendicular to the bases, then the cylinder is a right cylinder, if not then it is an oblique cylinder. Surface Area of a right cylinder S=L+2B or S= 2(pi)rh+2(pi)r^2 L=lateral base. B=base area Volume of a cylinder r=radius h=height V=Bh or V=(pi)r^2h

**EXAMPLE -- Find the Surface area of this cylinder with a r=20 and the h=10**
S=(pi)(20)(10)+2(pi)20^2 S=(pi)200+800(pi) S=1000(pi)

7.5- Surface Area and Volume of Cones
Vocab- Cone- is a 3-d 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, called the **vertex**. Altitude- of a cone is the perpendicular segment from the vertex to the plane of the base. Height- of the cone is the length of the altitude. Right Cone- if the altitude of a cone intersects the base of the cone at its center, the cone is a right cone, if not then it is an __oblique cone__. __Surface Area of a Right Cone__ S=L+B or S=(pi)rl+(pi)r^2 __Volime of a Cone__ V=(1/3)Bh or V=(1/3)(pi)r^2h For more help with surface area of a cone click [|HERE.]

__7.6 Surface Area and Volume of a Sphere__
Vocab- Sphere- is the set of all points in a space that are the same distance, r, from the given point known as the center of the sphere VOLUME- V= (4/3)(pi)r^3 SURFACE AREA- S=4(pi)r^2 ACTIVITY--> for an activity about volume of a sphere to practice click the link below http://www.aaamath.com/geo79-volume-sphere.html V=4/3(pi)8^3 V=4/3(pi)512 V=2144.66 For more help on this unit- surface area and volume. click the link below- http://www.math.com/school/subject3/lessons/S3U4L2GL.html
 * EXAMPLE-- Find the Volume of the sphere if the diameter=16**

Another link to help with Surface area and volume that we visited in math- click the link below http://www.shodor.org/interactivate/activities/SurfaceAreaAndVolume/?version=1.5.0_06&browser=MSIE&vendor=Sun_Microsystems_Inc.