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=**bibr107 Chapter 9 link**= == =**7.1 Surface Area & Volume**=

**Surface Area & Volume Formulas:**
Key: -//S// = surface area. -//l// = length. -//V// = volume. -//w// = width. -//h// = height.

s=2lw+2wh+2lh and v=lwh **[rectangular prism]** s=6s2 And V= s3 **[cube]**

//Surface Area: Think of an object, any shape. The entire total of the surfaces that aren't touching another surface, can be counted for the surface area.

[|Theres Even a Surface Area Calculator!] [|Volume]// = = =7.2 Surface Area & Volume of Prisms=

include both bases within the planes to be perpendicular
 * Altitude of a prism**= segments with endpoints that are




 * Height of a prism**=The height is the same length of the altitude.

//Parts: S-Surface Area L-Lateral Area// B-Base Area p-perimeter h-height
 * Surface Area Of A Right Prism**

S= L+2B or S= hp + 2B

So lets say for example, you have a right prism. The lateral area of the prism is 10. The base of the prism is 5. Using the SA formula, Solve.

S=10+2(5) S=10+10 S=20

V=lwh Because Base, B is the same as lw. There is another way to use the formula though: V=Bh.
 * Volume of Right Prisms:**

//Example: The base of a right prism is 22. The height of// the prism is 4.

V=(b)(h) =(22)(4) V=88

With Lateral edges not being perpendicular to the bases, its hard to take a stab at one good surface area equation.
 * Volume of Oblique Prisms:**



//Example: Height=90 B=120

(90)(120)=Volume of oblique V=10800// Think about two solids, with equal heights. The only way the two solids can have equivalent volumes is if they are the same height and if all the cross sectional areas are equal [|Cavalieri's Principle [Explained]]
 * Cavalieri's Principle:**

V=Bh. Because V is the volume, h is the height, and B is the base area.
 * Volume of a Prism:**

//Height=4.5 And Base Area=2// V=(4.5)(2) V=9 =7.3 Surface Area & Volume of Pyramids=

All lateral edges are equal to each other, the altitude crosses the base at its center. [|Triangular Pyramid] Triangular/Pentagonal/Hexagonal
 * Pyramid:** A polyhedron containing a base, and three &+ lateral faces.
 * Base:** A polygon
 * Vertex of the Pyramid:** Lateral faces all go to a vanish point and meet at a single vertex, called..
 * Base Edge:** common edges within lateral faces
 * Lateral Edge:** where two lateral faces meet, or cross.
 * Altitude:** The perpendicular Segment from the point of vertex to the plane of the base[Of a pyramid].
 * Height:** The equal length from the altitude[Of a pyramid].
 * A Regular Pyramid:** A regular polygon=its base. Congruent Isosceles triangles=lateral faces.
 * The Slant Height:** Altitude length of lateral faces.

S=surface area L=lateral area B=base area p=perimeter of base l[cursive, lowercase]=slant height
 * Surface Area of a Regular Pyramid:**

S=L+B or S=1/2lp+B.

//Example: L=13 p=18 B=3

S=1/2(13)(18)+3=120// V=volume h=height B=base area
 * Volume of a pyramid:**

V=1/3 Bh. h=5 b=9

V=1/3 (9)(5) The Volume=45

=7.4 Surface Area & Volume of Cylinders=

It's image that is reflected across is on a parallel plane, with a //Lateral Surface attaching the top to the bottom.// connecting the top to the bottom, also can be mistaken for the height. bottom, connecting the entire object together An oblique Cylinder is not a Right Cylinder.
 * Cylinder:** A cylinder is a complete solid circular object, think of a can of soup.
 * Lateral Surface:**The curved surface of a cylinder or cone
 * Bases:**The circular region [top & bottom] form faces of the cylinder
 * Altitude:**[Of a cylinder]A segment, or line up and down
 * Height:**The same as the altitude
 * Axis:**The segment in the center of the top and
 * Right Cylinder:** Axis isn't perpendicular
 * Oblique Cylinder:**If not that^, then its oblique.

=Prisms:= =Cylinders:=



S=surface area L=lateral face B=base area r=radius h=height
 * Surface Area of a Right Cylinder:**

S=L+2B or S=2rh+2r2

//Example:// radius=3 height=8

2(3)(8)+2(3^2) =207.345 V=volume r=radius h=height B=base area
 * Volume of a Cylinder:**

V=Bh or V=r2h.

//Example:// radius=2 height=6

V=(2^2)(6)=75.4

A Net for A Cylinder:


=7.5 Surface Area & Volume of Cones=

the bottom. A curved **lateral face** runs up and down the right and left sides, connecting the entire shape together, to the base.The point where everything meets is the **vertex**. the middle connecting the vertex to the base base of the cone in the middle. If not, it is an
 * Cone:** It is 3 dimensional, that has a circular **base** on
 * Altitude:** The perpendicular line running down
 * Height:** The altitude
 * Right Cone:** If the height, or altitude crosses the
 * __Oblique cone__**.

S=surface area L=lateral area B=base area r=radius l[cursive,lowercase]=slant height
 * Surface Area of a Right Cone:**

S=L+B or S=rl+r2

radius=9cm height/altitude=7cm slant height=2cm

(9)(2)+(9^2)=**311.017cm2**

V=volume r=radius h=height B=base area
 * Volume of a Cone:**

V=1/3Bh or V=1/3r2h

//Example: Radius=7 height=12 1/3(7^2)(12) V=615.75// [|¡Volume of a cone!]


 * A net for a cone:**

=7.6 Surface Area & Volume of Spheres=

the sphere, every point around the circle has the same distance, or radius[midway point].
 * Sphere:** There is one center point in the middle of

V=volume r=radius
 * Volume of a sphere:**

V=4/3r3

Radius=4 So, V=4/3(4^3) Volume= 268.082

S=surface area r=radius
 * Surface area of a sphere:**

S=4r2

Radius=7 So, S=4(7^2) Surface Area= 615.752

= = =7.7 Three-dimensional Symmetry=


 * •May be reflected across planes

__Revolutions in coordinate space:__** If you were to rotate a figure on its axis, you would keep receiving a sequence pattern of shapes.

[|Three-dimensional HELP!]

[|3D box-GAME!] [|Triangle Test-GAME!]
 * GAMES:

Volume and Surface Area of a triangular prism

Length=8cm Width=7cm height=7cm**

=392 cubic cm
 * Volume=l x w x h

Surface Area=2lw x 2wh x 2lh**
 * =1229312

Volume and Surface Area of a pyramid

Volume and Surface Area of a cylinder

Volume and Surface Area of a cone

Volume and Surface Area of a sphere**