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 * neje511 chapter 9 link

Chapter 7- Surface Area And Volume** Objectives: //Look at different ratios of volume and surface area.// //Make the concepts of maximizing volume and minimizing surface area.//
 * __Chapter 7.1…__**

//Key:// //S=surface area// //V=volume// //L=length// //W=width// //H=height//

Formula for the Surface Area and Volume of a RIGHT RECTANGULAR PRISM:

S=2lw+2wh+2lh and V=lwh

Formula for the Surface Area and Volume of a CUBE:

S=6s2 and V=s3

Define and use a formula for finding the surface area of a right prism, volume of a right prism, and the volume of a right or oblique prism.
 * __Chapter 7.2__**
 * Section Summary:**

__Altitude____-__ a segment that has endpoints in the planes that have the bases and is perpendicular to both of the planes. __Height-__ the length of an altitude in a prism
 * //__Vocabulary…__//**

S=L+2B or S=hp+2B
 * SURFACE AREA OF A RIGHT PRISM…**

V=Bh
 * VOLUME OF A PRISM…**

Two solids have equal volumes if the two solids have **equal heights** and the cross sections formed by every plane parallel to the bases of the two solids have **equal areas.**
 * CAVALIERI’S PRINCIPLE…**

//A company’s freezer in the shape of a right rectangular prism has dimensions of 110 x 50 x 7 feet. Given that one gallon of juice equal// =.134 cubic feet, how many gallons of water will the freezer hold? Given 1 gallon of juice= 8.33 pounds, how much will the juice weigh? V= Bh=lwh=(110)(50)(7)=38,500 feet V=38,500/.134= 287,313 gallons Weight=(287,313)(8.33)=2,393,317 pounds.
 * //EXAMPLE…//**
 * SOLUTION…**
 * The volume of the freezer can be found by using the volume formula.**
 * To approximate the volume in gallons, divide by .134.**
 * To approximate the weight, multiply by 8.33.**


 * __Chapter 7.3__

Objectives...** __//**Vocabulary**//__
 * 1) Using & defining a formula for the surface area of a regular pyramid.
 * 2) Using & defining a formula for the volume of a pyramid.
 * Pyramid- polyhedron that has a base
 * Base- polyhedron
 * Lateral Face- triangles that share onthe base is a vertex
 * Vertex Of The Pyramid- the lateral faces that share on vertex
 * Base Edge- the one edge that the lateral face and base share
 * Lateral Edge- the intesection of 2 lateral faces
 * Altitude- perpedicular segment from the plane of the base to the vertex
 * Regular Pyramid- a pyramid in which the base is a regular polygon and has lateral faces the are conguent isosceles triangles
 * Slant Height- the lengthes of the altitude of aregular pyramid's lateral face

//**PYRAMIDS ARE NAMED BY THE SHAPE OF THEIR BASE...** TRIANGULAR PYRAMIDS have a triangular base.//

RECTANGULAR PYRAMIDS have a rectangular base.



PENTAGONAL PYRAMIDS have a pentagonal base. HEXAGONAL PYRAMIDS have a hexagonal base.

Chapter 7.4 Objectives: Use and define the formula for the surface area and volume of a right cylinder.

VOCAB: Cylinder- solid that consists of a circular region and its translated image on a parallel plane with a lateral surface connecting the circles. Altitude (of a cylinder)- segment that has endpoints in the plans containing the bases and is perpendicular to both planes. Height (of a cylinder)- length of an altitude Axis (of a cylinder)- segment joining the centers of two bases. Right cylinder- if the axis of it is perpendicular to the bases Oblique cylinder- if the axis of it is NOT perpendicular to the bases

S=L+2B or S=2[pi]rh+2[pi]r2
 * SURFACE AREA OF A RIGHT CYLINDER…**

V=Bh or V=[pi]r2h
 * VOLUME OF A CYLINDER…**

Chapter 7.5 Objectives: Use and define the formula for the surface area and volume of a cone.

Vocab: Cone- 3-dimensional figure that has a circular base and a curved lateral surface and connects the base to a point (vertext) not on the plane of the base. Vertex- the single point that is not on the plane of the base Right cone- if the altitude intersects the base of the cone at the center Oblique cone- if the altitude DOES NOT intersect the base of the cone at the center.

S= L+B or S=[pi]rl+[pi]r2
 * SURFACE AREA OF A RIGHT CONE**

V=1/3 Bh or V=1/3 [pi]r2h
 * VOLUME OF A CONE**

Chapter 7.6

1.volume of triangular prism-1/2lwh

2.surface area of triangular prism-SA =2B + Ph [P= perimeter of the base]

3.volume of a pyramid- (1/3) **b**h

4.surface area of pyramid-SA = B + n(1/2s//l//)

5.volume of a cylinder-**b** h = [pi] r^{2} h

6.surface area of a cylinder-S = 2prh + 2pr2

7.volume of a cone- (1/3) **b** h = 1/3 [pi] r^{2} h

8.surface area of a cone-SA=[pi]r^{2}+[pi]rs

9. volume of a sphere-(4/3) [pi] r^{3}

10.surface area of a sphere-4 [pi] r^{2}