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Chapter 9 page by Joel S.

[|Over all help wiht SA] =7.1 Surface area and voulme=

The surface area (S), and volume (V), of a right rectangular prism with length (//L),// width (//w//), and height (//h//) are //S= 2lw+2wh+2lh// V//= l//wh//.// see examples below =7.2 Surface Area and Volume Of Prisms= An **altitude** of a prism is a segment that has endpoints in the planes containing the bases and that is perpendicular to both planes. The //S// of a right prism with lateral area (//L//), base area (//B//), perimeter (//p//), and height (//h//), is S=L+2B or S= hp+2B (V) of a prism with height h and base area B is V= Bh
 * Height** of a prism is the length of an altitude
 * Surface area of a right Prism:**
 * Volume of a Prism:**

see examples and pics below
 * [|Cavalier's Principle]:** two solids have equal heights and the cross sections fromed by every plane parallel to the bases of both solids have equal area then the two solids have equal volumes.

=7.3 Surface Area and volume of Pyramids= A pyramid: is a polyhedron with a base and three or more lateral faces. The lateraly faces are triangles that share a single vertex called the vertex of the pyramid A base ledge: is the edge that each lateral face has in common wiht the bass. A latral edge: is the intersection of two lateral faces altitude is the perpendicular segement from the vertex to the plane of the base height: is the length of its altitude. Regular pyramid: a pyramid whose base is a regular polygon and whose lateral faces are congruent isoceles triangles. Slant height: the length of an altitude of a lateral face of a regular pyramid.

Surface area of a regular pyramid
S= L+2B or S= ½//L//p + B

Volume of a pyramid
V= 1/3 Bh where V is the volume, B is the base area, and h is the height.

=7.4 Surface area and volume of cylinders=

Cylinders- an object that has 2 circular bases that are translated images of each other. Lateral surface- a cylinder's curved surface. Bases- the two circular regions of a cylinder. Altitude- a perpendicular line or a polygon that is perpendicular to the vertex and the opposite base of the vertex. Height- is the Altitude's length of a polygon. Axis- a segment or point that connects the centers of the bases of a cylinder. Right Cylinder- a cylinder with an axis that is perpendicular to its base. Oblique Cylinder- any cylinder that does not have an axis that is perpendicular to its base.

Surface area of a Right Cylinder
S= L+2B or S= 2π rh+2π r² where L is the lateral surface, B is the base area, r is the radius, and h is the height.

Volume of a Cylinder
V= Bh or V= π r²h where V is the volume, B is the base area, r is the radius, and h is the height. see examples below = =

=7.5 Surface area and volume of cones= [|More help] Cone- a 3-D shape that has a circular base and has a vertex opposite the base, Base- the circular section on the bottom of the cone. Lateral surface- curved surface in this case a cone. Altitude- a perpendicular line or segment or a polygon that is perpendicular to the vertex and the opposite base of the vertex. Height- is the Altitude's length of a polygon. Right cone- any cone that has an altitiude that interests at the center of its base. Oblique cone- any cone that does not have an altitiude that interests the base at its center. Slant height of a cone- the radius of a sector of any cone. see examples and pics below

Surface area of a right cone
S= L+B or S= πr//L//+πr² where S is the surface area, L is the lateral area, B is the base area, r is the radius, and //L// is the slant height.

Volume of a cone
V= 1/3 Bh or V= 1/3πr²h where =7.6 Surface area and Volume of spheres= [|help with SA of spheres] Sphere - any set of points that are equal in distance from the given point known as the center of the sphere. Annulus- is a circular or ring like structure, that is the region of space between two circles in a single plane that have the same center but have different radii.

Volume of a Sphere
V=4/3πr

Surface area of a sphere
S= 4πr² examples below Examples of Sa's and V's Triangular prism: Surface area S=L+2B ex. B=1/2 (5.2)(6)=15.6 P=6+6+6=18 L=12(18)=216 So.. S=216+2(15.6)=~247.2units2 .

Voulme V=bh V=(6)(6)(12)=432units3

Pyramid

ex. Surface area S=L+B s=4(1/2)(8)(6.5)=104+8(squared)=168meters2

Volume: V=1/3Bh V+64(squared)(6.5)=4102.5meters3

Cylinder Surface area S= 2(pie)rh+2(pie)r(squared)

S=2(3.14)(6.5)(6)+2(3.14)6.5(squared)=510.25Ft2 voulme V=(pie)r(squared)h V=(3.14)6.5(squared)(6)=795.99ft3

Cone surface area S=L+B l=30 and 2=14 (pie)(30or l)=94.2pie L=14/30(94.2pie)=138.03pie B=(3.14)(14(squared))=615.44pie B+L=615.44+138.03=753.47ft2

voulme V=1/3(pie)r(squared)h v=1/3(3.14)(6.5(squared))(6)265.33ft3

Sphere H=10 D=30 Surface area S=4(pie)r(squared) S=4(3.14)15(squared)=2826units2 Voulme V=4/3(pie)r(cubed) V=3/4(3.14)15(cubed)=662.34units3