kammor

Chapter 7
7-1 objectives: Ratio surface area to volume maximizing and minimizing surface area

Surface area and volume formulas surface area rectangular prism-S=2lw+2wh+2lh cube- S=6s² volume rectangular prism- V=lwh cube- V=s³ example:find the surface area of a rectangular prism and a cube, then find the volume. rectangular prism. S=2x7x8+2x8x3+2x7x3 S=112+48+42 S=202units² V=7x8x3 V=168units³ cube S=6x10² S=600units² V=10³ V=1000units³ http://www.mathsisfun.com/geometry/cuboids-rectangular-prisms.html http://www.mathsisfun.com/geometry/hexahedron.html http://www.mathsisfun.com/geometry/prisms.html

7-2 objectives: find the surface area of a right prism find the volume of a right prism Cavalieri's Principle formula for oblique or right prisms Surface Area of a Right Prism S=L+2B or S=hp+2B Volume of a Prism V=Bh Cavalieri's Principle if two solid objects have the same height, then they will have the same area and volume. example: find the surface area and volume of a right prism. volume V=Bh B=7sq cm h=5cm V=7x5 V=35units³ Surface Area S=hp+2B S=10x32+2x28 S=696units² http://www.regentsprep.org/Regents/math/geometry/GG2/PrismPage.htm http://www.algebralab.org/lessons/lesson.aspx?file=Geometry_3Dcylindersprisms.xml http://library.thinkquest.org/20991/geo/solids.html Try the quiz at the end, this will help out with prisms, pyramids, cylinders, spheres, and cones. pretty much what we will be covering here.

7-3 objectives: define the surface area of a regular pyramid. define the volume of a regular pyramid surface area of a regular pyramid S=L+B or S=½lp+B volume of a pyramid V=1/3Bh example: find the surface area and volume of a regular pyramid. S=½x8x18+6 S=78units² V=1/3x6x20 V=39.99units³ http://library.thinkquest.org/20991/geo/solids.html try the quiz at the end.

7-4 objectives: define the surface area of a right cylinder define the volume of a right cyliner surface area of a right cylinder S=L+B or S=2x3.14xrh+2x3.14xr² Volume of a cylinder V=Bh or V=3.14xr²h example: find the volume and surface area of a cylinder. S=2x3.14x8x19+2x3.14x8² S=192,230.2976units² V=3.14x8²x36 V=7,234.56units³ http://www.algebralab.org/lessons/lesson.aspx?file=Geometry_3Dcylindersprisms.xml http://www.math.com/school/subject3/lessons/S3U4L4GL.html follow the steps at the top of the page. http://library.thinkquest.org/20991/geo/solids.html

7-5 objectives: define the surface area of a cone define teh volume of a cone surface area of a right cone S=L+B or S=3.14xrxl+3.14xr² volume of a cone V=1/3Bh or V=1/3x3.14xr²h example: find the surface area and the volume of a cone. S=3.14x5x9+3.14x5² S=3,611units² V=1/3x3.14x5²x25 V=654.16units³ http://www.math.com/school/subject3/lessons/S3U4L4GL.html. follow the step on the top of the page http://library.thinkquest.org/20991/geo/solids.html

7-6 objectives: define the surface area of a sphere define the volume of a sphere volume of a sphere V=4/3x3.14xr³ surface area of a sphere S=4x3.14xr² example: find the surface area and a volume of a sphere. V=4/3x3.14x8² V=267.946units³ S=4x3.14x8³ S=6,430.72units³ For extra help with prisms in math check out these sites: http://www.math.com/school/subject3/lessons/S3U4L2GL.html keep clicking the next button and read through the pages. http://www.math.com/school/subject3/lessons/S3U4L4GL.html Follow the steps on the top of the page. http://library.thinkquest.org/20991/geo/solids.html

1. Volume of a triangular prism EX: The base of a triangular prism is 14 the height is 10. So you take V=Bh, V=14*10= V=140units³ 2. Surface area of a triangular prism EX: The height is 10, the perimeter is 37, and the base is 14. So you take S=hp+2B S=10*37+2*14= 370+2*14= 370+28= S=398units² 3. Volume of a pyramid EX: The base of a pyramid is 10, and the height is 20. So you take V=1/3Bh V=1/3*10*20= 1/3*200= V=66.666units³ 4. Surface Area of a Pyramid EX: A lateral area of 8, a perimeter of 216, and a base of 6. So you take S=1/2lp+B S=1/2*8*216+6= 1/2*1728+6= 1/2*1734= S=867units² 5. Volume of a cylinder EX: Has a radius of 6 and a hight of 25. So you take V=3.14r²h. V=3.14*6²*25= 3.14*36*25= 3.14*900= V=2826units³ 6. Surface Area of a cylinder EX: Has a radius of 6, and a hight of 25. So take S=2*3.14rh+2*3.14r². S=2*3.14*6*25+2*3.14*6²= 942+226.08= S=1168.08units² 7. Volume of a cone EX: With a radius of 8, and a hight of 18. So take V=1/3*3.14r²h. V=1/3*3.14*8²*18= 1/3*3.14*64*18= 1/3*3.14*1152 1/3*3617.28= V=1205.76units³ 8.Surface Area of a cone EX: If a cone has a raidus of 8, a lateral face of 10, find the volume using this equation.S=3.14*rl+3.14*r² S=3.14*8*10+3.14*8²= 251.2+200.96= S=452.16units² 9.Volume of a Sphere EX: What is the volume of a sphere with a radius of 9. Use V=4/3*3.14r³ V=4/3*3.14*9³= 4/3*3.14*729= 4/3*2289.06= V=3052.08units³ 10. Surface Area of a Sphere EX: What is the surface area of a sphere with a radius of 9. Use the formula S=4*3.14r². S=4*3.14*9²= 4*3.14*81=

S=1017.36units²