3pentri

The Following Will Contain Information About Surface Area and Volume of Solid Figures
**Section #1** __Objectives for Section 1__ - To look at ratios of Surface Area to Volume - To figure out how to maximize volume while minimizing surface area

To get a feel of Surface Area and Volume heres a cool link to [|check out]

__SURFACE AREA AND VOLUME FORMULAS__ Surface Area = S Volume = V Length = L Width = W Height = H

__Surface Area and Volume Formulas For a Right Rectangular Prism__ Surface Area = 2xLxW + 2xWxH + 2xLxH Volume = LxWxH

__Surface Area and Volume Formulas For a Cube__ Surface Area = 6xs² Volume = s³



__Examples__

A food distributing company is designing a new box to pack food into, They want to know which box will have the largest surface area for selling purposes.

__Dimension of Box A__ Height = 4 in. Width = 2 in. Length = 2.5 in. The volume = 20 cubic inches

__Dimension of Box B__ Height = 5 in. Width = 1 in. Length = 4 in. The volume = 20 cubic inches

__Solution To Our Problem!__ Both boxes have a volume of 20 cubic inches. The Surface Area of box A is 2(4)(2.5)+ 2(2)(2.5)+ 2(2)(4) = __46 sq. inches__

The Surface Area of box B is 2(5)(4)+ 2(1)(4)+ 2(1)(5) = __58 sq. inches__

Therefor, box B has a larger Surface Area and will have more eye appeal when the company try's to sell their product.

__Surface Area and Volume of Prisms__ Key Words: Altitude of a Prism - Is a segment thats endpoints are in the planes containing the bases and that is perpendicular to both planes. Height of a Prism - is the length of the altitude. A link to get you thinking a little more about [|prisms]
 * Section #2**

__Surface Area of a Right Prism__ S=L+2B OR S=HP+2B S = Surface Area L = Lateral Area B = Base Area P = Perimeter H = Height

__Cavalieri's Principle__ If two solids have equal volumes, then the two solids have equal heights and the cross sections formed by every plane parallel to the bases of both solids have equal areas.

__Volume of a Prism__ V= BH V = Volume B = Base Area H = Height



__Example of Surface Area and Volume of Prisms__ Your at a local zoo looking into the aquarium. You notice it's in the shape of a right rectangular prism with dimensions 115 x 55 x 12 feet. Find the volume of the aquarium using volume formula V = BH = LWH

Solve : Volume Formula V = BH = LWH So, 115x55x12 = 75,900 cubic feet

__Surface Area and Volume of Pyramids__
 * Section #3**

Nice feel to how this involves [|pyramids]

Vocab Words: Pyramid - A polyhedron consisting of a base Lateral Faces - Triangles that share a single vertex Vertex Of The Pyramid - Single vertex of the whole polyhedron Base Edge - Lateral Faces have 1 common edge with the base called the Base Edge Lateral Edge - The intersection of 2 lateral faces is the lateral edge Altitude - The perpendicular segment from the vertex to the plane of the base Height - The height of a pyramid is the length of its altitude Regular Pyramid - A pyramid whose base is a regular polygon and whose lateral faces congruent isosceles triangles Slant Height - The length of an altitude of a lateral face of a regular pyramid is the slant height

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Surface Area of a Regular Pyramid __ Surface Area = S Lateral Area = L Base Area = B Perimeter of Base = P Slant Height = H

S = L + B or S = 1/2hp+b

__Volume of a Pyramid__ Volume = V Height = H Base Area = B

V = 1/3Bh

__Exercise:__ Find the volume of the pyramid given base edge = 700ft height = 400ft

Solution: V = 1/3bh = 1/3 (700)(400) = 1/3 x 280000 = 93333.33 cubic feet

__Surface Area and Volume of Cylinders__
 * Section #4**

Website to get a feel for [|Cylinders]

Key Words: Cylinder - Solid that consists of a circular region and its translated image on a parallel plane Lateral Surface - What connects the circles Bases - Two parallel images of cylinder Altitude - A segment that has endpoints in the planes containing the bases and is perpendicular to both planes Height - The length of an altitude Axis - Segment joining the centers of the two bases Right Cylinder - When axis of cylinder is perpendicular to the bases Oblique Cylinder - When axis of cylinder is not perpendicular to the bases

__Surface Area of Right Cylinder Formula__ Surface Area = S Lateral Area = L Base Area = B Radius = R Height = H

Formula : S = L+2B OR! S = 2πRH + 2π r²

__Volume of a Cylinder Formula__ Volume = V Radius = R Height = H Base Area = B

Formula = BH OR! V = π r²H

__Surface Area and Volume of Cones__
 * Section #5**

Website to learn about cones! Even [|NASA]  uses these equations!

Key Words: Cone - 3 dimensional figure Base - Circular bottom of figure Lateral Face - Connects base to all other parts of cone Vertex - Single point controlling every part in cone Altitude - Perpendicular segment from the vertex to the plane of the base Height - Length of the altitude Right Cone - When altitude of cone intersects the base of the cone at its center Oblique cone - When altitude of cone does NOT intersects the base of the cone at its center



__Surface Area of a Right Cone Formula__ Surface Area = S Lateral Area = L Base Area = B Radius = r Height = H

Formula = S = L+B OR! S = π rH + π r²

__Volume of a Cone Formula__ Volume = V Radius = r Height = H Base Area = B

Formula = V = 1/3BH OR! V= 1/3 π r²H

__Surface Area and Volume of Spheres__
 * Section #6**

Key Words: Sphere - Is the set of all points in space that are the same distance from a given point Annulus - The ring shaped figure in the cylinder

__Volume of a Sphere Formula__ Volume = V Radius = r

Formula = V=4/3 π r³

__Surface Area of a Sphere Formula__ Surface Area = S Radius = r

Formula = S=4 π r²

__Three-Dimensional Symmetry__
 * Section #7**

Three dimensional symmetry can be be explained through pictures, it's when an image is exactly the same on both sides like a butterfly for instance.



This happens a lot with nature as well.

