pletho

chapter 9 tplesha 7.1 surface area and volume __Rectangle__ __Cube__ S=2lw+2wh+2lh S=6s² V=lwh V=s³ l=1 w=2 h=1 V=lwh V=1x2x1 V=2

7.2 surface area and volume of prisms surface and volume of right rectangular prism S=2//L//w+2wh+2Lh and V=Lwh suface are and volume for cube with sides k is S=6k² and V=k³ volume of a prism V=BH B=12 H=2 V=12x2 V=24 surface area of a right prism S=L+2b (or) S=HP+2B S= surface area L= lateral area B= base area H= height altitude - a segment that has endpoints in the planes containing the bases and that is perpendicular to both planes. height - how tall it is. __Cavalieri's Principle--__ If two solids have equal height and the cross sections formed by every plane parellel to the bases to both solids have equal area's, then the two solids have equal volume.

7.3 Surface Area and Volume of Pyramids Pyramid - polyhedron consisting of a base and three or more lateral faces. the lateral faces are triangles that meet at one point. Base - polygonal face that is opposite the vertex. lateral face - a face of the prism that is not the base. vertex of the pyramid - base edge - an edge that is part of the base of a pyramid; each lateral face has one edge in common with the base. lateral edge - the intersection of two lateral faces of a polyhedron. altitude - a segment from the vertex perpendicular to the plane of the base. height - how tall it is from the center of the base to the point. regular pyramid - a pyramid whose base is a regular polygon and whose lateral faces are congruent isosceles triangles. slant height - length of the side. surface area of a regular pyramid-- L=lateral area B=base P=perimiter of base L=slant height S=L+B or S=½LP+B volume of a pyramid-- V=½BH B=6 H=6 V=6x6x½ V=18 7.4 Surface Area and Volume of Cylinders [|math formula's] cylinder -- a solid thta consist of a circular region + its translated image on a parallel plane wit lateral suface connecting the circles. lateral surface -- the faces formed by the circular region. bases---bottom of the cylinder. altitude --- endpoints in the planes containing the bases + it's pendicular to both planes. height -- length of altitude axis -- segment joining the centers of the two bases right cylinder -- if the axis perpendicular to the bases. oblique -- if it isn't then it's oblique cylinder surface area of a right cylinder -- S=L+2B or S=2x3.14rh + 2x3.14r² Volume of a cylinder -- V=Bh or V=3.14r²h 7.5 surface area and volume of cones cone -- three dimentional figure consist of a circular base and curved lateral Base -- the bottom circle lateral Surface -- connects the base to the single point. altititude -- perpendicular segment from the vertex to the plane of the base. height -- length of altitude. Right Cone -- altitude is perpendicular to the base. oblique -- it's not perpendicular slant height of a cone -- point to base on side. Surface area of right cone -- S=L+B or S=3.14rl+3.14rh Volume of a cone - V=1/3BH or V=1/3x3.14r²h 7.6 surface area and volume of spheres __[|sphere picture]__ sphere -- set of points some 'r' distace from same point. Annulus -- circular region of sphere Volume of a sphere -- V=¾3.14r³ surface area of a sphere -- S=4x3.14r²

h= 6ft s= 5.5ft l= 7ft. 1 V=Bh B=(1/2bh)2.75x6 B=16.5 16.5x6 V=99ft.

2 S=L+2B

3 V=½BH s=2 l=6 a²+b²=c² 1+6=7 2x2=4 7x4x½=14

4 S=L+B 7+14=21

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