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Chapter 7__**

7.1 **Surface Area and Volume

//(l=length,w=width,h=height)//**
 * Surface area of a right rectangular prism** - 2lw+2wh+2lh
 * Volume of a right rectangular prism** - l*w*h
 * Surface area of a cube** - 6*s^2 (s = side length)
 * Volume of a cube** - s^3

7.2 **Surface Area and Volume of Prisms

Altitude -** the height of anything above a given planetary reference plane
 * Height -** distance upward from a given level to a fixed point


 * (S=Surface area, L=Lateral area,B=Base area,p=Perimeter,h=Height

Surface Area of a Right Prism -** (S= L+2*B) or (S= h*p+2*B) A few more examples and a better explanation of prisms can be found [|here].
 * 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.
 * Volume of a Prism -** (V=B*h)

7.3 **Surface Area and Volume of Pyramids

Pyramid -** A polyhedron consisting of a base, and three or more
 * Lateral Faces -** Are triangles that share a single vertex
 * Base Edge -** Each lateral face has one edge in common with the base, called the base edge
 * Lateral Edge -** The intersection of two lateral faces
 * Regular Pyramid -** Is a pyramid whose base is a regular polygon and whose lateral faces are congruent isosceles triangles
 * Slant Height** - Is the length of an altitude of a lateral face of a regular pyramid


 * Surface Area of a Regular Pyramid** - (S= L+B) or (S= 1/2*l*p+B)
 * Volume of a Pyramid** - (V= 1/3*B*h)

(Example of a regular pyramid) http://math.about.com/library/blmeasurement.htm

7.4 **Surface Area and Volume of Cylinders**


 * Cylinder -** Is a solid that consists of a circular region and its translated image on a parallel plane
 * Altitude -** A segment that has edpoints in the planes containing the bases and is perpendicular to both planes
 * Height -** Is the length of the altitude
 * Axis -** Is the segment joining the centers of the two bases
 * Right Cylinder -** If the axis of a cylinder is perpendicular to the bases
 * Oblique Cylinder -** If the axis of a cylinder is not perpendicular to the bases


 * Surface Area of a Right Cylinder -** (S= L+2*B) or (S= 2*3.14*r*h + 2*3.14*r^2)
 * Volume of a Cylinder -** (V= B*h) or (V= 3.14*r^2*h)

7.5 **Surface Area and Volume of Cones**


 * Cone** - Three-dimensional 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
 * Vertex** - The single point not in the plane of the base
 * Altitude** - Is the perpendicular segment from the vertex to the plane of the base

(Example of a right cone) http://math.about.com/library/blmeasurement.htm
 * Surface Area of a Right Cone** - (S= L+B) or (S= 3.14*r*l + 3.14*r^2)
 * Volume of a Cone** - (V= 1/3*B*h) or (V= 1/3*3.14*r^2*h

Some more examples of right cones and a better explanation can be found [|here].

7.6 **Surface Area and Volume of Spheres**


 * Sphere -** Is the set of all points in space that are the same distance
 * Annulus -** The region between two circles in a plane that have the same center but different radii


 * Volume of a Sphere -** V= 4/3*3.14*r^3
 * Surface Area of a Sphere -** S= 4*3.14*r^2

Here is a link to a great example of finding the surface area and volume of Spheres. http://www.gomath.com/algebra/sphere.php

1. __Ex. Volume of triangular prism__ A right triangular prism has the side lengths 5, 12, and 13. To find the volume

2. __Ex. Surface Area of triangular prism__

3. __Ex. Volume of pyramid__ A pyramid with a rectangular base has the length and width equal to 5in. and a height of 8in. First we need to find the base area so we do 5*5 which equals 25. We then take the base area of 25 and multiply it by the height. So 25*8 =200. Lasty we need to multiply 200 by 1/3. 200*1/3= 66.67in.^3

4. __Ex. Surface Area of pyramid__

5. __Ex. Volume of Cylinder__ A right cylinder has a radius of 10cm and a height of 15cm. To find the volume we must first find the area of the base, to do so we just simply plug the radius of 5 into the area of a circle formula (3.14*5^2) =78.5cm. The volume of a cylinder formula is B*h so now we just plug 78.5 into B. 78.5*15= 1177.5cm^3

= = 6. __Ex. Surface Area of Cylinder__ A right cylinder has a radius of 10cm and a height of 15cm. To find the surface area we do (2*3.14*5*15 + 2*3.14*5^2). Which comes out to 628cm^3

7. __Ex. Volume of a cone__ A right cone has a radius of 6cm and a height of 8cm and a slant height of 10cm. To find the volume we simply plug the measurements into the volume of a cone formula. (1/3*3.14*6^2*8 = 376.9cm^3)

8. __Ex. Surface Area of a cone__ A right cone has a radius of 6cm and a height of 8cm and a slant height of 10cm. To find the Surface area we plug the measurements into the formula for surface area of a cone. (3.14*6*10 + 3.14*6^2 = 301.6cm^2)

9. __Ex. Volume of a sphere__ A sphere has a diameter of 10m. To find the volume we use the volume of a sphere formula. To get the radius of the sphere we simply divide the diameter by two which gets us the 5 for the radius. The final equation would be (4/3*3.14*5^3) = 523.5m^3

10. __Ex. Surface Area of a sphere__ A sphere has a diameter of 10m. To get the radius to be used in the formula we just divide the diameter in half to get 5. To find the surface area we simply use the surface area of a sphere formula. (4*3.14*5^2) = 314.1m^2