mehjac

MeJa522 Chapter 9 Link

=CHAPTER 7=

Surface Area And Volume Formulas: The Surface area S, and the Volume V, of a right rectangular prism with length L, width W, and height H are: S=2LW+2WH+2LW and V=LWH The Surface area and Volume of a cube with side s are: S=6s2 and V=s3 Learn: Take several blocks(1x1, 1x2, 1x3, 1x4) and connect them together so you have different lengths Of 1,2,3, and 4. Then make a chart finding the surface area and the volume (use formulas above) and then find the ratio of surface area to volume by dividing surface area by volume. Example: Length=4 Height=5 Width=4 S=2(4x4)+2(5x4)+2(4x5) V=4x5x4 S=32+40+40 V=20x4 S=112 V=80
 * http://argyll.epsb.ca/jreed/math9/strand3/3107.htm( this site has all the formulas for the different shapes to find the surface area and volume)**
 * 7.1-Explore Ratios of surface area to volume, Develop concepts of maximizing volume and minimizing surface area.**

Altitude-A segment that has endpoints in the planes containing the bases and that is perpendicular to both planes. Height- Length of an altitude. The surface area, s, of a right prism with lateral area L, base area B, perimeter p, and height h, is: S=L+2B or S=hp+2B 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 areas, then the two solids have equal volume. The Volume, V, of a prism with height h and base B is: V=Bh Pyramid-A polyhedron consisting of a base and three or more lateral faces. Base-Polygon Lateral face- Triangle that shares a single vertex Vertex of a pyramid- vertex shared by lateral faces Base edge-The edge that the lateral faces have in common with the base Lateral Edge- Intersection of two lateral faces Altitude-Perpendicular segment form the vertex to the plane of the base Height- Length of altitude Regular pyramid-A pyramid whose base is a regular polygon and whose lateral faces are congruent isosceles triangles. Slant height- Length of and altitude of a lateral face of a regular pyramid
 * 7.2- Define and use the formula for the surface area and volume of a right prism and use Cavalieri’s principle to develop a formula for the volume of a right oblique prism.**
 * 7.3-Define and use the formulas for the surface area and volume of a regular pyramid.**

The Surface area, S, of regular pyramid with lateral area, L, base area, B, perimeter of the base p, and slant height L is: S=L+B or S=1/2Lp+B The Volume V, of a pyramid with height h, and base area B is: V=1/3Bh

Cylinder-Solid that consists of a circular region and its translated image on a parallel line Lateral Face-Connects 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-Length of altitude Axis-Segment joining the center of the two bases Right cylinder-If the axis of a cylinder are perpendicular to the bases then it’s a right Cylinder Oblique- If its not the above
 * 7.4-Define and use a formula for the surface area of a right cylinder, define and use a formula for the volume of a cylinder.**

The surface area S, of a right cylinder with lateral area L, base area B radius r, and height h is: S=L+2B or S=2 rh+2 r2 The Volume, V, of a cylinder with radius r, height h, and base area B is: V=Bh or V= r2h


 * 7.5-Define and use the formula for the surface area and volume of a cone.**

Cone-Three-dimensional 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 Vertex- Single point not in the plane of the base Altitude- The perpendicular segment from the vertex to the plane of the base Height- Length of the altitude Right cone- If the altitude of a cone intersects the base of the cone at its center Oblique cone- If its not the above The volume V, of a cone with radius r, height h, and base of area B is: or

The surface area, S, of a right cone with lateral area L, base of area B, radius r, and slant height L is: S=L+B or Example: Take a waffle ice cream cone and measure the base and the height. Put the numbers into the formula to get the volume and surface area. For example: Height=6 Base=3 V=1/3x6x3 V=1/3x18 V=6


 * 7.6-Define and use the surface area and volume of a sphere.**

Sphere-Set of all points in space that are the same distance r, from a given point know as the center of the sphere.

The Volume V, of a sphere with radius r, is:

The surface area S, if a sphere with radius r, is:

http://www.gomath.com/algebra/sphere.php( This site will give you practice on finding the surface area and volume of spheres)

V=Bh V=4x3 V=12 2. Surface area of a triangular prism- Lateral area=6 Base area=4 S=6+2x4 S=6+8 S=14 3.Volume of a pyramid- Height=7 base area= 8 V=1/3Bh V=1/3(7x8) V=18.66 4. Surface area of a pyramid- Lateral area= 6 base area=6 S=L+B S=6+6 S=12 5. Volume of a cylinder- Height=9 Base area=8 V=BH V=9x8 V=72 6. Surface area of a cylinder- lateral area=8 Base area=10 S=L+2B S=8+2(10) S=28 7. Volume of a cone- Height=5 Base area=4 V=1/3Bh V=1/35x4 V=6.66 8. Surface area of a cone- Lateral area=12 Base area=14 S=L+B S=12+14 S=26 9. Volume of a sphere-Radius=4 V=4/3 V=4/3 V=268.08 10. Surface area of a sphere-Radius=7 S=4 r2 S= 4pie49 S=615.75
 * 1) Volume of a triangular prism- Height=3 Base=4