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=Fian32 links chapter9= = = = = = = =**7.1 Surface area and Volume**=

[|SURFACE AREA: rectangular prism] Flickr VOLUME SURFACE AREA: cube
 * Rectangular based prism
 * Base shape:** Rectangle, length 'L' and width 'W'
 * Area of base:** L × W
 * Perimeter of base:** 2(L+W)
 * Surface area** = 2LW + 2(L+W)H ||
 * V = //l × w × h//**
 * **Surface Area of a Cube = 6 s****2** ||

=7.2 SURFACE AREA AND VOLUME OF PRISMS= Flickr a segement that has endpoints in the plane containing the bases and that is perpendicualr to both planes.
 * Altitude-**

the length of an altitude
 * Height-**

Surface Area = Lateral area + Area of two ends (Lateral area) = (perimeter of shape **b**) * L Surface Area = (perimeter of shape **b**) * L+ 2*(Area of shape **b**)
 * SURFACE AREA OF A RIGHT PRISM:**

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 solids have equal volumes
 * CAVALIERI'S PRINCIPLE:**

=**[|7.3 Surface Area and Volume of pyrmaids.]**= < Rectangular Pyramid Flickr

A polyhedron in which all but one of the polygonal faces intersect at a single point known as the vertex of the pyramid
 * __Definition of pyramid__**

__**Definition of base**__ The polygonal face that is opposite the vertex

__**Definition of lateral face**__ The faces of a prism or pyramid that are not base

__**Definition of vertex of the pyramid**__ The point where all lateral faces of the pyramid intersect

__**Definition of base edge**__ An edge that is part of the bas of a pyramid; each lateral face has one edge in common with the base

__**Definition of regular pyramid**__ A pyramid whose base is a regular polygon and whose lateral faces are congruent isosceles triangles

In a regular pyramid, the length of an altitude of a lateral face
 * __Definition of slant height__**

__**Surface area of a regular pyramid**__ S-surface area L-lateral area B-base area p-perimeter of the base //l// - slant height

S= L + B or S= .5//l//p + B

V-volume h-height B-base
 * __Volume of a pyramid__**

V=1/3Bh

__**Different types of pyramids**__ The pyramids are named by the shapes of their bases. (ex. a pyramid with a base that has 10 sides would be a decagonal pyramid)

=[|7.4 SA and volume of cylinders]= A solid that consists of a circular region and its translated image in a parallel plane with a lateral surface connecting the circles
 * __Definition of Cylinder__**

The curved surface of a cylinder or cone
 * __Definition of lateral surface__**

__**Definition of axis**__ The segment joining the centers of the two bases

__**Definition of a right cylinder**__ A cylinder whose axis perpendicular to the bases

__**Definition of oblique cylinder**__ A cylinder that is not a right cylinder

__**Surface area of a right cylinder**__ S-surface area L-lateral area B-base area r-radius h-height

S = L + 2B or S = 2(3.14)rh + 2(3.14)r²

__**Volume of a cylinder**__ V-volume r-radius h-height B-base area

= =

=7.5 SA and Volume of cones= [|SA and Volume of cones (extra help)]

Flickr

__**Definition of a cone**__ A 3-D figure that 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, called the vertex

__**Definition of vertex**__ A point where the edges of a figure intersect

__**Definition of right cone**__ A cone in which the altitude intersects the base at its center point

__**Oblique cone**__ A cone that is not a right cone

__**Surface area of a right cone**__ S-surface area L-lateral area B-base area r-radius l-slant height S L + B or S (3.14)rl// + (3.14)r²

__**Volume of a cone**__ V-volume r-radius h-height B-base area V =1/3 Bh or V= 1/3 (3.14)r²h 7.6 SA and volume of spheres = = = = =7.6 Surface Area and Voume of Spheres= Flickr __**Definition of sphere**__ The set of points in space that are equidistant from a given point known as the center of the sphere

__**Definition of annulus**__ The region between two circles in a plane that have the same center but different radii __Volume of a sphere__ V-volume r-radius V = 4/3(3.14)r³

__**Surface area of a sphere**__ S-surface area r-radius S = 4(3.14)r²

1.volume of triangular prism-
 * Extra stuff:**

B=4,h=2

V=Bh V=8

2.Surface area-(same triangular prism as above) L=4

S=L+2B 4+4*2 4+8 S=12

3.Volume of a pyramid L=5 B=6 h=3

S=L+B 5+6 S=11

4.Surface area of a pyramid-(using pyramid from above) V=1/3Bh 1/3 6*3 V=1/3 18 V=6

5.Volume of a cylinder- B=5 h=2 L=8

V=Bh 5*2 10 V=10

6.Surface area of a cylinder.

S=L+2B 8+2*5 8+10 S=18

7.Volume of a cone.

B=8 h=2 L=4

V=1/3Bh 8*2 16 V=1/3(of)16

8.Surface area of a cone.

S=L+B 4+8 S=12

9.Volume of a sphere r=3 V=4/3(pie)r^3 3.14*9