scuabi

scab518 chapter 9 link

Chapter 7 The objectives of this chapter are to allow you to learn about the following: Surface area and volume Surface Area and Volume of Prisms Surface Area and Volume of Pyramids Surface Area and Volume of Cylinders Surface Area and Volume of Cones Surface Area and Volume of Spheres Three-dimensional Symmetry

Chapter 7 section 1 the objectives are to explore ratios of surface area and volume, along with developing concepts of maximizing volume minimizing surface area.

Now what are the volume and surface area? 2 times( 5 times 8)** 2 times( 5 times 10) = 100**
 * Say L=****5, W=****8 and H = 10
 * 2 times(10 times 8) =160
 * Thats how you get the surface area**

5 times 8 times 10**
 * Now to get the volume you:

[|scuabiCube]

Surface Area and Volume formulas: S=2LW+2HW+2LH and V=LWH

[|Surface Area and Volume of Prisms] this site was created by: Jim Reed

Chapter 7. section 2 The objectives in this section are to define and use a formulas for finding the surface area and volume of a right prism. Also you will learn Cavalieri's principle for developing a formula to find the volume of an right or oblique prism.

[|ScuabiPrism]

=5 and B= 9 Find the Volume
 * H**

=5, B9 and P= 10 Find the Surface Area
 * H**

Altitude: Is the prism segement that has endpoints in planes containing bases that are perpendicular to both of the planes.

Height: Is the same length as the altitude.

Surface Area of a Right Prism:
 * S=**L+2B or SHP+2B

Volume of a Prism:
 * V=Bh**

Cavalieri's Principle: If two solids have equal heights and the cross sections formed by every plane parallel to the bases of both solids have equal
 * 1) areas, than the two solids have equal volumes.

Chapter 7 section 3 The objectives of this section are to use the formulas to find the surface area and volume of a pyramid.

[|scuabiPyramid]

=L= 11, B=7= =Find the Surface Area.= =H= 11, B=7 Find the Volume.= =**V**= 1/3 times 11 times 7= =[|Space figures and basic solids] this site was made by Math League Pyramid:= =A pyramid is a polyhedron consisting of a base with more then three or more lateral sides. Base: is a polygon with three or more lateral sides. Lateral faces: Are triangles that share a single vertex, that vertex is a called the vertex of a pyramid. Vertex of a pyramid: Each lateral face has on edge in common. Base Edge: Is where all of the lateral faces share on edge with the base. Lateral Edge: Is the intersection of two lateral faces. Altitude: Is where the pyramid is perpendicular segment from the vertex to the plane of the base. Height: Is the pyramids length from the altitude. Regular Pyramid: is a pyramid that has a base that is a regular polygon and whose lateral faces are congruent isosceles triangles. Slant Height: Is the length of the altitude of a lateral face of a regular pyramid.= =Surface Area: **S**= L+B or S1/2 LP+B= =Volume: **V**= 1/3Bh= = = =Chapter 7 section 4:= =This section you will learn to use a formulas for the surface area and volume of a cylinder.= =**R**= 3 H=4= =Whats the Surface Area? Whats the Volume? **S**= 2 times **π** **times 3 times 4 + 2 times** **π** **times 3 squared V=** **π** **times 3^2 times 4** [|Surface Area and Volume of a Cylinder] this site was created by Algebra Lab Cylinder: Is a solid object that consists of a circular region and its translated image on a parrallel planes. Lateral Surface: Is the connecting of the circles. Bases: Faces formed by the circular region and its translated image. Altitude: Segment that has endpoints in the planes containing the bases and is perpendicular to both planes. Height: Is the length of the altitude. Axis: Is the segment joining the centers of the two bases. Right Cylinder: perpendicular to the bases. Oblique Cylinder: in its not perpendicular then its Oblique. Surface Area of a Right cylinder: **S** =2πrh+2πrˆ2 Volume of a Cylinder: **V**= πR2h=[|scuabiCylinder] =Chapter 7 section 5 the objective of this section are to use the formulas for surface area and volume to find that of a cone. Cone: 3-dimensional figure Base: circular and curved **L**= 2 and R=6 Find the surface area and volume?=

[|Cone]

Lateral Surface: that connects to the base to the single point not in the plane of the base Altitude: perpendicular segment from the vertex to the plane. Height: Is the length of the Altitude Right Cone: Altitude intersects base of the cone at center. Oblique Cone: if it doesn't do that of a Right Cone. Slant Height: Radius of a cone.

Surface Area
 * S=**L+B or SπRL+πR^2

Volume
 * V=1/3 π R^2 H**

Chapter 7 section 6 The objectives of this section are to use the formulas for the surface area of a sphere and volume.

[|scuabiSphere]


 * r=8 find the surface area and volume**

8^2 times 3.14 times 4 to get the surface area**
 * 3.14 times 8^3 then times by 4/3 to get the volume

Sphere: is a set of all points in a space that has the same distance from a given point that is known as the center of a sphere. Annulus: is a ring shaped figure in a cylinder. Volume of a Sphere: Surface Area: Vocabulary:
 * V=4/3πR3**
 * S=4πR2**

Section 1 answers Surface area................. 340 Volume........................400

Section 2 answers Surface Area...............60 Volume...................45

Section 3 answers Surface Area..................18 Volume...................2.3

Section 4 answers Surface Area...............753.6 Volume...............339.12

Section 5 answers Surface Area............131.88 Volume.................75.36

Section 6 answers Surface Area..............803.84 Volume...............2143.57

Examples:

1. Volume of Triangluar Prism L=4, W=8 and H=5 S= 2 * 4 * 8 +2 * 5* 8 + 2 * 4* 5 = 23240
 * //To get this you take 2 times 4 times 8 and get and add 5 times 8 times 2 and get and then you add 4 times 5 times 2 and get 23240//**

2. Surface Area of a Triangular Prism L=2, H=3 and W= 7 V= 2 * 7 * 3 = 42
 * //To get this you just do as it show do length times width times height and you get your answer//**

3. Volume of a Pyramid =S= L+B 4. Surface Area of a Pyramid 5.= =Volume of a Cylinder R= 7 and H=9 **π * 7 * 2 * 9** 395.64 //you take the radius times 2 times pi times the height. So first you can take 7 ( radius) times 2 then times that by Pi (3.14) and 43.96 times 9 and get the answer of 395.64.// 6. Surface Area of a Cylinder **2** * **π * 3 * 8 + 2 * π * 3^2**=2877.2448 //What you do is take 2 times Pi (3.14) and get 6.28 and times that by 3 and get 18.84 then times by 8 and you get 150.72. You then add 2 times Pi (3.14) times 3 squared and get 2877.2448.// 7. Volume of a Cone L=6 and B= 4 1/3 * **π * 2^2 * 6** =25.12. //To get this answer you take Pi (3.14) times 2 squared times 6 and get 75.36. Then you times that by 1/3 to do that times the number first by 1 and then divide that by 3 and you should get 25.12.// 8. Surface Area of a Cone B= 6 and L=8 π * 3 * 8 + π * 3^2 =471 to get this you take Pi (3.14) times 3 times 8 and get 75.36 plus Pi ( 3.14) times 3 squared and get 471. 9. Volume of a Sphere **R**= 9 π * 9^3=2289.06 times 4/3 and get 3052.08 To get this answer you take the Radius 9 cubed times Pi ( 3.14) and times that by 4 and then divide that answer by 3. 10. Surface Area of a Sphere. **S** =4πR2 R= 7 π * 7^2= 153.86 * 46769.84