roejoh

rojo35 ch 9 link
=__CHAPTER 7__=

7.1
=Surface Area and Volume= __objectives:__
 * 1) explore ratios of surface area to volume.
 * 2) develop the concepts of maximizing volume and minimizing surface area.

[|Surface Area] and [|Volume] Formulas
The surface area and volume of a rectangular prism. surface area and volume of a cube.
 * S=2lw+2wh+2lh and V=lwh.
 * S=6s^2 and V=s^3

7.2
=Surface Area and Volume of Prisms= __objectives:__ 1. define and use a formula for finding the surface area of a right prism. 2. define and use a formula for finding the volume of a right prism. 3. use cavaliers principle to develop a formula for the volume of a right or oblique prism.


 * BOLD WORDS.**
 * Altitude- is a segment that has endpoints in the plane containing the bases and that is perpendicular to both planes.
 * Height- is the length of an altitude.

Surface Area of Right Prisms

 * S= L+2B or S= hp+2B

Cavaliers 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, the the two have equal volumes.

Volume of a Prism

 * V=Bh.

7.3
=[|Surface Area and Volume of Pyramids]= __objectives:__
 * 1) Define and use a formula for the surface area of a regular pyrammid.
 * 2) Define and use a formula for the volume of a pyramid.


 * BOLD WORDS.**
 * pyramid- is a polyhedron consisting of a base, wich is a polygon, and three or more lateral faces.
 * lateral faces- are triangles that share a singe vertex, called the vertex of the pyramid.
 * vertex of the pyramid- are triangles that share a singe vertex.
 * base edge- the lateral face has one edge in common with the base called base edge.
 * altitude- is the perpendicular segment from the vertex to the plane of the base.
 * height of pyramid- is the length of its altitude.
 * regular pyramid- is a pyramid whose base is a regular polygon and whose lateral faces are congruent isosceles triangles.
 * slant height- 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=1/3Bh

7.4
=Surface Area and Volume of Cylinders= __objectives:__ cylinder- is a solid that consists of a circular region and its translated image on a parallel plane, with a lateral surface connecting the circles. bases- the faces formed by the circular region and its translated image are called the bases.
 * 1) Define and use a formula for the surface area of a right cylinder.
 * 2) define and use a for the volume of a cylinder.
 * BOLD WORDS.**

Surface Area of a Right Cylinder

 * S=2pie rh+2pie r^2

Volume of a Cylinder

 * V=pie r^2h

7.5
__objectives:__ cone- a three-dimensional figure that consists of a circular base and a curved lateral surface that connects the base to a single point not in te plane of the base, called the vertex.
 * 1) Define and use the formula for the surface area of a cone.
 * 2) Define and use the formula for the volume of a cone.
 * BOLD WORDS**

Surface Area of a Right Cone

 * S=pie rl+pie r^2

Volume of a Cone

 * V=1/3pie r^2h

7.6
__objecties:__ sphere- is the set of all points in space that are the same distance annulus-ring shaped figure in the cylinder
 * 1) Define and use the formula for the surface area of a sphere
 * 2) Define and use the formula for the volume of a sphere
 * BOLD WORDS**

Volume of a Sphere

 * V=4/3pie r^3

Surface Area of a Sphere

 * S=4pie r^2

plug them all into your calculater and you get the answer.
 * 1) surface area of a triangle- if its height is 7 base area 36 base perimeter is 23 so S= hp+2B so S=(7)(23)+2(36) so you just put that into the your calculater and it gives you the surface area.
 * 2) volume of a triangle- V=Bh so V=(36)(7)
 * 3) volume of a pyramid-what is the volume of a pyramid if thel is 6 and the area of the base=9 and the perimeter of the base=12 and the height was 8. so V=1/3bh V=1/3(9)(8)
 * 4) surface area of a pyramid- S=1/2 lp+B S=1/2(6)(12)+9
 * 5) volume of a cylinder- what is the volume of a cylinder if its height is 7 and its radius is 4? V=pie r^2(7) V=pie(4)^2(7)
 * 6) surface area of a cylinder- SA=2pie rh+2pie r^2 so SA= 2pie(4)(7)+2pie(4)^2
 * 7) volume of a cone- what is the volume of a cone if it has a radius of 4 a height of 8 and a l of 12. V=1/3 pie r^2h so V=1/3pie(4)^2x(8)
 * 8) surface area of a cone- S= pie rl +pie r^2 so S=pie(4)(12)+pie(4)^2
 * 9) volume of a sphere- what is the volume if the radius it 6. so V=4/3pie r^3 then V=4/3pie(6)^3
 * 10) surface area of a sphere- S=4pie r^2 so plung in r S=4pie(6)^2