trenic

__**//trenicchapter9link//**__

7.1

OBJECTIVES: explore ratios of suface area to volume.

develope the concepts of maximizing voume and minimizing suface area.

__Bold words:__ none in this section

__Blue boxes:__

the surface area, s and volume, v of a right rectangular prism with length l, width and height h are
 * surface area and volume formulas:**

s=2lw+2wh+2lh and v =lwh

the surface area s and volume v of a cube with side s are:

s=6s^3

Example: cube with a length of 4in. and width of 4 in and height of 4 in find the surface area and volume.

so... SA=2lw+2lh+2wh and v=lwh

2x4x4+2x4x4x2x4x4=

2x4=8 ; 8x4=32 ; 32x3=96 ; so the surface area of the cube is 96in^2

v=4x4x4

4x4=16 ; 16x4=64 ; so the volume=64in^3

cube picture came from [|Http://www.minerals.net/glossary/images/cube.gif]

7.2

ojectives:

define and use a formula for finding the surface area of a right prism.

define and use formula for finding the volume of right prism

use cavalieri's principle to develope a formula for the volume of a right or oblique prism

bold words:

altitude- the height from the base of an oject to its pinnacle

height- the length from base to pinaccle

blue boxes:

SA of right prism: the SA of a right prism with lateral area L and base area B perimeter P and height H S=L+2B or S=HP+2B

Calalieri's Principle: If two solids have equal height s adn the cross sections formed by every plane parallel to the bases of both solids have equal areas, then the two solids have equal volumes.

V of prism: The volume, V, of a prism woth height h and base area B is V=Bh

example:

length of prism is 5 base is 10 and perimeter is 20 and lateral area is 20 20+2(5) = 30 so thirty units squared

7.3

objectives:

define and use a formula for the SA of a regular pyramid

define and use a formula for the volume of a pyramid

Bold words:

Pyramid- a three dimensional object with three to four faces and 1 base

base- the bottom of any given figure

vertex of the pyramid- the angle measure from one corner of an object to another

base edge- the length of one of the base edges

lateral edge- the length of the face on any given object

altitude- the length from the base to the pinnacle

height- the length of an object from bottom to top

regular pyramid- a three or four sided object with 90 degree angles for the base

slant height- the height of one of the faces on a given object

Blue boxes:

SA of a rectanular pyramids:

the SA 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= 1/2 LP + B

Volume of a pyramid: the area inside of the pyramid

The volume V of a pyramid with height h and base area B is V=1/3 BH

example: v= 1/3 b x h h =10 b= 30 soo... area = 100 units cubed

7.4

objectives: define and use a formula for the SA of a right cylinder

define and use a formula for the volume of a right pyramid

bold words: cylinder: a three dimensional object that it is circular and has lateral surface to connect the circles lateral surface: the space that is 2 dimensional and connects things together Bases: the bottom of any given object altitude: the length of the base to the pinnacle of the object height: the measure of something from top to the bottom axis: where the spaces meet eachother right cylinder: a clinder that has a right angle in it oblique cylinder: any cylinder that doesnt have axis pependicular to the bases

blue boxes: SA of right cylinder: SA of right cylinder with lateral area L base area B and radius r and height h S =L +2B or S= 2 pie RH +2 pie R squared

Volume of cylinder:

The volume v of cylinder with radius r and height h and base b is: V=Bh or V= pie r squared h

formulas: none

example:

v= b x h base =5 height= 10 so.. area = 50 units cubed

7.5 objectives: define and use the SA for a cone

define and use the volume formula for a cone