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Tyler's Chapter 9 Objectives__
 * //__7.1__//** __Surface Area and Volume

__**Formulas for a cube**__ __**//7.2//**__
 * Explore ratios of surface area to volume *
 * Develop the concept of maximizing volume and minimizing surface area
 * SA = 2lw + 2wh + 2lh
 * V = lwh

Surface Area of a Right Prism
The surface area S, of a right prism with lateral area L, base area B,perimeter p, and h is S=L+2B or S=hp+ 2b.

Cavalieri's Priniple
If two solids have equal hights and the cross selections formed by evry plane parallel to the bases of both solids have equal aareas, then the two soilds have equal volumes.

Volume of a prism
The volume, v, of s prism with hight h and base area B isV=Bh.

A cube is a block with all angles that is the same size in height, width and depth. The sides of a cube are squaress. The edges are straight lines. The corners are at right angles. There are 8 corners, 12 edges and 6 sides. The volume of a cube is the length of the edge //E// multiplied by itself three times: E x E x E. A cube is one of the easiest shapes in space, and something that is shaped like a cube is also called "//cubic."//

Pyramid-** polyhedron consisting of base, and 3 more lateral edges.
 * __//7.3//__ __Definitions:__
 * Base**- A polyhedron.
 * Lateral Face**-triangles that share a single vertex, called vertex of pyramid
 * Vertex of the Pyramid**- Lateral faces are triangles that share a single vertex.
 * Base Edge-** Each lateral face has one edge in common w/ the base is called base edge.
 * Lateral Edge**- Intersection of two lateral faces
 * Altitude-** Altitude is perpendicular segment from vertex to plane of base.
 * Height-** Length of altitude.
 * Regular Pyramid**- Pyramid whose base is a regular polygon whose lateral faces are congruent to the iscoceles triangle.
 * Slant Height**- Length of altitude of lateral face of regular pyramid.

__**Example 1.**__ Find the surface area of a regular square pyramid whose slant height is //l// and whose base edge is //s.//

S= L + B S=4 (1/2sl) + s^2 ~ This can be written as follows: S= 1/2 L (4s) + s^2...because 4s is the perimeter of the base. S= 1/2 lp + s^2

The surface area, S of a regular pyramid w/ lateral area L, base area B, perimeter of base P, and slant height L is... S= L+B or S= 1/2 Lp+ B.
 * __Surface Area of regular pyramid:__**


 * //__7.4 Surface Area and Volume of Cylinders__//

Objectives:** 1.Define and use the formula for the surface area of a rigt cylinder 2. Define and use a formula for the volume of a cylinder. S= L+B or S=2(pi)rh+2(pi)r^2
 * Cylinder:** is a solid that consists of a circular region.
 * Surface Area of a Right Cylinder.**
 * volume of a cylinder:** V=Bh or V=(3.14)r^2h

__**//7.5 Surface area and volume of cones//**__ Objectives:D efine and use the formula for hte surface area of a cone Define and use the formula for the volume of a cone. =1/3 Bh or V= 1/3(3.14r^2h) =//L + B or S//= //**3.14 rl + 3.14 r^2**//
 * 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, called the vertex.- Textbook.
 * Volume of a cone:** The volume, V, of a cone with radius //r,// height h, and base area B is V
 * Surface area of right cone:** The surface area, S, of a right cone with lateral area L, base area B, radius //r//, and slant height l is...
 * S**




 * __7.6__**


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

__VOCABULARY:__

 * **__Sphere-__** The set of all points in space that are the same distance, r, from a given point known as the center of the sphere.
 * **__Annulus-__** A ring shapped figure in a cylinder.



__FORMULAS:__
V=Bh, V=(7)(5), V=35u^3 V=1/3Bh ,base area= 1/2Bh,=1/2(4)(3) B=6 H=8 V=1/3(6)(8) = 16u^3 SA=1/2lp + B 1/2(6)(16) + 24=72u^2 diameter 8 height 10 V=πr^2h π(8)^2(10) 640π or 2009.6u3 diameter 6 height 8 SA= 2πrh + 2πr^2 2π(3)(8) + 2π(3)^2 48π + 18π 64π or 200.96u2 V=1/3πr^2 =1/3π(7)^2 16.17π or 50.77u^3
 * 1.** Volume of a triangular prism
 * 1.** Volume of a triangular prism
 * 2.** Surface area of a triangular prism
 * 3.** Volume of a pyramid
 * 3.** Volume of a pyramid
 * 3.** Volume of a pyramid
 * 4.** Surface area of a pyramid
 * 4.** Surface area of a pyramid
 * 5.** Volume of a cylinder
 * 5.** Volume of a cylinder
 * 6.** Surface area of a cylinder
 * 6.** Surface area of a cylinder
 * **7.** Volume of a cone radius 7 height 10

100π or 314u^2
 * 8.** Surface area of a cone slant height 15 radius5 SA= πrl + πr^2 π(5)(15) + π(5)^2 75π + 25π
 * 8.** Surface area of a cone slant height 15 radius5 SA= πrl + πr^2 π(5)(15) + π(5)^2 75π + 25π

radius = 9 V=4/3πr^3 =4/3π(9)^3 36π or 113.04u^3
 * 9.**Volume of a sphere
 * 9.**Volume of a sphere

radius = 22 SA=4πr^2 =4π(22)^2 1936π or 607.04u^2
 * 10.** Surface area of a sphere
 * 10.** Surface area of a sphere