nelbri

nebr32 link to chapter 9
=Section 7.1=

Formulas for surface area and volume
Surface area and volume of a right rectangular prism Surface area and volume of a cube [|//surface area and volume of everything//] [|surface area and volume]This page will help you with volumes and surface areas for evrything in this chapter. Scroll down for the information.
 * //S=2Lw+2wh+2Lh and V=Lwh//
 * //S=6s² and V=s³//

=Section 7.2 Prisms=

Definitions:
__Altitude-__ a segment with endpoints in the planes containing the bases and that is perpendicular to both of the planes. __Height-__ the lengh Surface area of a right prism S=surface are L=lateral area B=base area P=perimeter H=height //S=L+2B or S=hp+2//S=L+2B or S=hp+2

Cavalieri's Principle
In order fot two solids to have equal volumes they have to have equal height and the cross sections formed by every plane parallel to the bases have to have equal areas The Volume of a Prism V=volume h=height B=base area //V=Bh//

=Section 7.3 Pyramids=

Definitions:
__Pyramid-__In a polyhedron all of the faces but one of the faces intersects at a single point known as the vertex of the pyramid. __Base-__The face of a polygon that is opposite of the vertex __Lateral face-__faces of a pyramid or prism that are not the bases __Base edge-__Its part of the base of a pyramid that is an edge;each of the lateral faces has only one edge in common with the base __Lateral edge-__In a polyhedron, its the intersection of two lateral faces __Altitude-__segment from the vertex that ia perpendicular to the plane on the base __Height-__A polygons length of an altitude __Regular pyramid-__A pyramid with a base that is a regular polygon and that that lateral faces are congruent isoseles triangles __Slant height-__A regular pyramid, the length of an altitude of a lateral face

Surface area of a regular pyramid
L=lateral face B=base area P=perimeter of the base l=slant height

//S=L+B or S=1/2lp+B//

Volume of a pyramid
V=volume H=height B=base area

//V=1/3Bh//



= = =Section 7.4 Cylinders=

Definitions:
__Cylinder-__a soid that has a circular region and its translated image in a parallel plane with a lateral surface connecting the circles __Lateral surface-__Its the curved surface on a cone or cylinder __Bases-__faces formed by the circular region and its translated image __Altitude-__a segment thats from the vertex thats perpendicular to the plane of the base __Height-__The length of an altitude of a polygon __Axis-__a segment that joins the centers of the two bases __Right cylinder-__A cylinder that has its axis perpendicular to the bases __Oblique cylinder-__its a cylinder that is not a right cylinder

Surface Area of a Right Cylinder
S=surface area L=lateral area B=base area r=radius h=height

//S=L+2B or S=2pierh+2pier²//

Volume of a Cylinder
V=volume r=radius h=height B=base area

//V=Bh or V=pier²h// [|cylinders]



=Section 7.5 Cones=

Definitions:
__Cone-__a three dimensional figure that has a circlular base and a lateral face __Base-__the circular face of a cone Lateral surface-The curved part of a cone or cylinder __Altitude-__A segment from the vertex thats perpendicular to the plane of the base __Height-__The lenght of the altitude __Right cone-__A cone, were the altitude intersects the base at its center point __Oblique cone-__A cone thats not a right cone __Slant height of a cone-__the radius of the sector

Surface area of a right cone
S=surface area L=lateral face B=base of area r=radius l=slant height

//S=L+B or S=pierl+pier²//

Volume of a cone
V=volume r=radius h=height B=base area

//V=1/3Bh or V=1/3pier²h//

[|cones]

=Section 7.6 Spheres=

Definitions:
Sphere-is the set of all points in space that are the same distance from a given point known as the center of the sphere Annulus-A ring,a shaped figure in the cylinder

Volume of a Sphere V=volume r=radius

//V=4/3pier³//

Surface Area of a Sphere S=surface area r=radius

//S=4pier²//



E=equation

Q=question A=answer S=how it is solved 1.Volume of a triangular prism E:V=1/2b triangle x h triangle x hxp Q:A triangular prism with a hight of 3 in., a length of 5 in.,and a weigth of 3 in. what is the volume? S: 1/2X5X3X3=22.5 A: The answer is 22.5 inches

2.surface area of triangular prism E:SA=2B+Ph or SA=L+2B Q: A triangular prism that has a base of 22 in., a height of 10 in., a lateral area of 12 in., and a perimeter of 18 in. what is the surface area? S:2X22+18X10 A:The answer is 224 inches

3.volume of pyramid E:V=1/3s²h Q:A pyramid with the base area of 15 m, and a height of 8 m what would the volume be? S:1/3X15X8 A: the answer is 40 m

4.surface area of pyramid E:S=L+B or S=1/2lp+B Q:A pyramid with the lateral area of 7, a base area of 10, a slant height of 12 what is the surface area, and a perimeter of 24? S:1/2X12X24+10 A: the answer is 154

5.volume of cylinder E:V=Bh or V+pier²h Q: A cylinder with a radius of 6, a height of 9, and a base area of 14 what would the volume be? S: 3.14X6²9 A:1017.88 6.surface area of cylinder S=L+2B or S=2pierh+2pier² 7.volume of cone V=1/3Bh or V=1/3pier²h 8.surface area of cone S=L+B or S=pierl+pier² 9.volume of sphere V=4/3pier³ 10.surface area of sphere S=4pier²