treely

trel215 Chapter 9 link __Chapter 7-1__
__Surface Areas and Volume Formulas 2-4__- __Rectangular prism-__ surface area, S volume, V lenght,L width, W height, H S= 2//LW//+2//WH//+2//LH// and V//LWH// __Cube-__ Surface Area-S Volume-V

Chapter 7-2
__Surface Area of a Right Prism__ - The surface area,S lateral area L base are a B perimeter p height h

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=== =//ex2-B//= 1/2(4)(31)=62p=20+31+27=78L=hp=40(78)=3120S=L+2B=3120+4(31)=3244+42=3286 __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 volumes. __Volume of a Prism__- volume, V height, h base, B V=Bh

Chapter 7-3 __Definitions__ Pyramid- is a polyhedron with a base, and three or more lateral faces Base- is a polygon Lateral Faces- are triangles that share the same vertex Vertex of a Pyramid- is a vertex that is shared by lateral faces Base Edge- is an edge that each lateral face has in common with the base Lateral Edge- is an edge that intersect the two lateral faces Altitude- is a perpendicular segment from teh vertex to the plane of the base Height- is the length of the altitude Regular Pyramid- is a pyramid with a base that is a regular polygon and lateral faces are congruent isosceles triangles Slant Height- is the lenght of an altitude of a lateral face of a reguglar pyramid

__Surface Area of a Regular Pyramid__ Surface Area-S Lateral Area-L Base Area-B Perimeter of base-p Slant height-l S=L+B or S1/2lp+B //ex3A roof of a ga//zebo is a reu//lar octagonal pyramid that has a base edge of 9 feet and has a slant height of 12 feet. Find teh area of the roof. If the cost of roofing cost $5.50 per square feet, what is the cost for the roofing material?L////1/2lp=1/2(12)(8*9)=432 square feet432*$5.50=$2,376.00// __Volume of a Pyramid__Volume-V Height-h Base Area-B V=1/3Bh

Chapter 7-4 Cylinder-has a circular region and its translated image on a parallel plane Lateral Surface- connects the circles Bases- faces that are formed by a circular region and a translated image Altitude- a segment that has endpoints in the planes containing the bases and that is perpendicular to both pla Height- lenght of altitude Axis- segment that joins the two bases in the center Right cylinder- when an axis is perpendicular to the base Oblique cylinder (2-4)- when an axis is NOT perpendicular to the base __Surface Area of a Right Cylinder__ Surface Area-S Lateral Face-L Base Area-B Radius-r height-h S=L+2B or S2(3.14)rh+2(3.14)r^2

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//The radius of a penny is 9.525 millimeters. The thickness of it is 1.55 millimeters.// //S=2(3.14)rh+2(3.14)r^2 S=2(3.14)(9.525)(1.55)+2(3.14)(9.525)^2=663.46 square millimeters// __Volume of a Cylinder__ Volume-V Radius-r Heigh Base Area-B V=Bh or V(3.14)r^2h



Chapter 7-5 Cone-has a circular base and a curved lateral face and is three-dimensional Base-has a circular base Lateral Surface-has a curved lateral surface Vertex-where the lateral surface connects at a point that is not in the plane of the base Altitdude-is a perpendicular segment that starts at the plane of teh base Height-lenght of altitude Right Cone when the altitude o the cone intersects the base at its center Oblique Cone- when the altitude does not intersect the base at the center __Surface Area of a Right Cone__ Surface Area-S Lateral Area-L Base Area-B Radius-r Slant Height-l S=L+B or S=(3.14)rl+(3.14)r^2 __Volume of a Cone__ Volume-V Radius-r Height-h Base Area-B V=1/3Bh or V=1/3(3.14)r^2h

Chapter 7-6 Sphere-points that are equidistant fromthe center of the sphere Annulus-region between two circles that have teh same center but different radii Surface Area of a Sphere __Surface Area-S__ Radius-r S=4(3.14)r^2 __Volume of a Sphere__ Volume-V Radius-r V=4/3(3.14)r^3

Questions 1-Volume of a triangular prism 2-Surface area of a triangular prism 3-the Volume of a pyramid 4-Surface area of a pyramid 5-Volume of a cylinder 6-Surface area of a cylinder 7-Volume of a cone(elyse) 8-Surface area of a cone 9-Volume of a sphere(elyse) 10-Surface area of a sphere