raukam

RaKa691

go here to learn more: http://www.mathsisfun.com/geometry/cuboids-rectangular-prisms.html
 * 7.1 Surface area and Volume**
 * Surface Area- S=2lw+2wh+2lh Surface area is the combinde area of all faces of an object.
 * Volume- V=lwh
 * example:
 * __**A cube with a side length of 5**__
 * SA=5x5x6
 * SA=150
 * V=5x5x5
 * V=125

> S=L+2B or S=hp+2B > V=Bh go here to learn more: http://www.mathsisfun.com/geometry/cuboids-rectangular-prisms.html
 * 7.2 surface area and volume of prisms**
 * Altitude- segment that has endpoints in the planes containing the bases and that isperpendicular to both planes
 * Height- length of the altitude.
 * Surface Area of a right prism- S(surface area) L(lateral heaight) B(base area) p(perimeter) h(height)
 * 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- The volume, V, of a prism with height,h, and base area, B, is:

http://commons.wikimedia.org/wiki/Image:PyramidDatePalms.jpg** go here to learn more: http://www.mathsisfun.com/geometry/pyramids.html
 * 7.3 surface area and volume of pyramids
 * Pyramid- a polyhedron consisting of a base, which is a polygon, and 3 or more lateral faces.
 * Vertex of a pyramid- single point every lateral edge connects to
 * Base edge- an edge of the base of the pyramid
 * Lateral Edge- intersection of 2 lateral faces
 * Regular Pyramid- pyramid with a base that is a regular polygon
 * Slant Height- altitude of a lateral face
 * Surface Area of a Regular pyramid-The surface area, S, of a regular pyramid with lateral area L, base area B, perimeter of the base p, and slant height l is:
 * S=L+B or S=1/2lp+B
 * Volume of a pyramid:
 * V=1/3Bh
 * Example:
 * __**a regular square pyramid with a lateral height of 2 and a base edge length of 4 and a height of 3**__
 * S=16+16
 * S=32
 * V=1/3x16x3
 * V=16

** go here to learn more: http://www.mathsisfun.com/geometry/cylinder.html
 * 7.4 surface area and volume of cylinders
 * Cylinder- a solid that consists of a circular region and its translated image on a parallel plane with a lateral surface connecting the circles.
 * bases- faces formed by the circular region and its translated image
 * axis- a segment joining the centers of the 2 bases
 * right cylinder- cylinder with the bases perpendicular to the altitude
 * oblique cylinder- cylinder with the bases not perpendicular to the altitude
 * Surface Area of a Right Cylinder- S=L+2B or S=2(pi)rh+2(pi)r^2
 * Volume of a cylinder-V=Bh or V=(pi)r^2h
 * example:
 * __**a cylinder with a radius of 10 and a height of 10**__
 * S=2x3.14x10x10
 * S=628
 * V=3.14x10^2x10
 * V=314x10
 * V=3140

http://commons.wikimedia.org/wiki/Image:Cones500.jpg go here to learn more: http://www.mathsisfun.com/geometry/cone.html
 * 7.5 Surface area and Volume of a prism**
 * Cone- 3D figure consisting of a circular base and a curved lateral face that connects the base to a single point in the plane of the base called the vertex
 * Altitude- the perpendicular segment from the ertex to the plane of the base.
 * Height- the length of the altitude
 * Right cone- vertex is centered over the base
 * Oblique cone- it isnt
 * SA of right cone- lateral area is L, base area is B, radius is r, slant height is s.
 * S=L+B or S=(pi)rs+(pi)r^2
 * V of a right cone
 * 1/3 B/h or V= 1/3(pi)r^2h
 * example:
 * __**a cone with a radius of 10 and a slant height of 10 and a height of 10**__
 * S=3.14x10x10+3.14x100
 * S=31.4+314
 * S=345.4
 * V=1/3x3.14x100x10
 * V=1033.3333

http://commons.wikimedia.org/wiki/Image:Golfball.jpg** go here to learn more: http://www.mathsisfun.com/geometry/sphere.html > a regular triangular prism with a height of 4 and a base edge of 2 and a base height of 2 > the base area is 4x2. times that by the height of 4 and you get the volume > V=8x4 > V=32 > a regular triangular prism with a height of 5 and a base edge of 4 and a base height of 3 > find the product of the base areas and add that to the lateral area > S=(5x5x3)+(4x3x2) > S=99 > A regular square pyramid with a base length of 2 and a height of 3 > Volume is 1/3 times the base area which is 2x2 times the height which is 3. The 1/3 and the 3 cancel out so it the volume equals 4 > V=1/3x2x2x3 > V=2x2 > V=4 > SA of a regular square pyramid with a slant height of 2 and a base edge of 4 > SA is 1/2 times the slant height 2 times the base perimeter of 16 plus the base area which is also 16 > S=1/2x2x16+16 > S=16+16 > S=32 > a cylinder with a base area of 100 and a height of 4 > the base area of 100 times the height of 4 equals the volume > V=100x4 > V=400 > A cylinder with a radius of 20 and a height of 5 > SA is pi times the radius 20 times the height 5 times 2 plus 2 times pi times 20 squared > S=2pi20x5+2pi400 > S=3140 > A cone with a height of 3 and a slant height of 5 > find the radius which is 4 square it and multiply that by 1/2 pi and 5 > V=4^2xpix5x1/2 > V=16xpix2.5 > V=40xpi > V=125.6 > a cone with a height of 3 and a slant height of 5 > find the radius which is 4 and multiply it by pi and by the slant height, 5. Add that to pi times 4^2 > S=pix4x5+pix4^2 > S=pix20+pix16 > S=62.8+50.24 > S=113.04 > Sphere with a radius of 3 > multiply 4/3 by 3^2 and then by pi > V=4/3x3^2xpi > V=4/3x9xpi > V=12xpi > V=37.68 > Sphere with a radius of 4 > multiply 4^2 by 4 and then by pi > S=4^2x4xpi > S=64xpi > S=200.96
 * 7.6 surface area and 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
 * Radius- distance from center of sphere to any part of the surface of the sphere
 * Annulus- A cylinder with a cone cut out of each base with the vertexes meeting at a single point in the center. The annulus has the same volume of a sphere with a diameter that is the same length as the annulus's height.
 * Volume of a Sphere:
 * V=4/3(pi)r^3
 * Surface Area of a Sphere:
 * S=4(pi)r^2
 * example:
 * __**a sphere with a radius of 10**__
 * V=4/3x3.14x10^3
 * V=4/3x3.14x100
 * V=4/3x3140
 * V=4186.666.....
 * S=4x3.14x10^2
 * S=4x3.14x100
 * S=4x314
 * S=1256
 * 1) **volume of a triangular prism:**
 * 1) **Surface area of a triangular prism:**
 * 1) **Volume of a pyramid:**
 * 1) **Surface area of a pyramid:**
 * 1) **volume of a cylinder:**
 * 1) **surface area of a cylinder:**
 * 1) **volume of a cone:**
 * 1) **surface area of a cone:**
 * 1) **volume of a sphere:**
 * 1) **surface area of a sphere:**