3rodjor

== = = [|http://flickr.com/photos/fri13th/156182821/sizes/o][|/] =The following is a discussion about Surface Area and Volume.= = = = = =A link to the volume and surface area of a sphere= =[|Cool link]=

The formulas for volume and surface area are.... for a right rectangular prism Let S= surface area, V=volume o and l= length w= width, h=height

S= 2lw + 2wh + 2lh and v=lwh

For a cube.... 2=6s² and v=s³ A person is trying to decide which cereal to buy. They want to choose the box with the most surface area. The one with the larger surface area has more cereal in it, which one sould the person buy? http://www.flickr.com/photos/roboppy/25116606/ http://www.flickr.com/photos/arnaoot/35829501/ 12 inches (h) 4 inches (w) ..................................3 inches (w) 8 inches (h) .........................box a 3 inches (l) .....................................................................................box b 6 inches (l)

both boxes have a volume of 144 cubic inches. the surface area of box a is 2(12) (3) + 2(4) (3) + 2 (4) (12) = 192 square inches

the surface area of box b is 2 (8) (6) + 2 (3) (6) + 2 (3) (8) = 180

box a has a larger surface area so the person should buy box a.

http://www.flickr.com/photos/petromyzon/62288675/

the **__height__** is the length of an altitude

Surface area of a right prism the surface area of a right prism is S = L + 2B or S = hp + 2B when b= base area and p= perimeter,

the volume of a prism is.. v = bh when v = volume, h = height and b = base area

cavalieri's principle states that 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 two solids have equal volumes example

http://www.flickr.com/photos/shirleyccs/444773686/

A swimming pool that is shaped like a right rectangular prism has the dimensions of 100 X 30 X 7 feet. Given that 1 gallon = 0.134 cubic feet, how many gallons will the swimming pool hold?

You can find the volume by doing v = bh = lwh = (100) (30) (7) = 21,000 cubic feet if 1 gallon = 0.134 cubic feet then you divide 21,00 by 0.134 and get your answer which is 156,716 gallons

http://www.flickr.com/photos/cathepsut/2108777251/

surface area and volume of pyramids

In the following text you will learn to use a formula for the surface area of a pyramid

use a formula for the volume of a pyramid

a pyramid is a polyhedron and has a base that's a polygon and three or more lateral faces. the vertex of the pyramid is the vertex that the lateral faces share. the lateral faces each have one edge incomon with the base and that's called the base edge. the intersection of two lateral faces if a lateral edge.

altitude of a pyramid= perpendicular segment from the vertex to the plane of the base

height of a pyramid = the length of the altitude

a regular pyramid is a pyramid whose base is a regular polygon and it's lateral faces are congruent isosceles triangles. All of the lateral edges are congruent and the altitude intersects the base at the center.

surface area of a regular pyramid s= surface area, L= lateral area b =base, perimeter of base = p and slant height = l s = L + B or s = 1/2lp + B

volume of a pyramid v= volume h = height and b = base v= 1/3 bh

here's an example that i found to better help me understand pyramids

[|Link to better understand pyramids]

example... find the volume of this pyramid http://www.flickr.com/photos/hakonlo/294072373/ ............................height = 400 .........................................................base = 650² v = 1/3 bh

1/3 (650²) (400)

the weight in pounds is 56,333,333 cubic feet X 166 lbs. per cubic foot so the volume in lbs of the pyramid is 9,407,666,611 lbs.

surface area and volume of cylinders http://www.flickr.com/photos/lochnessjess/1820701992/

in the following readings you will use the formula for the surface area of a cylinder and use a formula for the volume of a cylinder

cylinders are solids that have a circulra region, and it's translated image on a parallel plane. what connects the cirlces is a lateral surface

the faces of the cylinders are called the bases

the altitude of a cylinder is a segment that has endpoints in the planes containing the bases and is perpendicular to both planes.

the height in a cylinder is the length of the altitude.

the axis in a cylinder is the segment joining the centers of the two bases

if the axis of the cylinder is perpendicular to the bases, then the cylinder is a right cylinder. if not, then it's an oblique cylinder

the formula for surface area of a right cylinder

the surface area s of a right cylinder with lateral area, l base area, b and radius, r and height h is

s = l +2b or s = 2 π rh+ 2 π r²

the formula for volume of a cylinder is

for the formula, let v = volume, r = radius, h = height and b = base

v=bh or v = π r²h

[|a link to help better understand cylinders]

example... on a foreign planet, there are aliens whome are obsessed with building gigantic statues of tubes. help the Gorgons find the volume for this tube (excluding the arms) to see if their's is bigger than the rival Lorgans

http://www.flickr.com/photos/freeed/500554414/ .....................................height = 60 cubic feet .........................................................................................base = 30 cubic feet

v = bh so the volume is 1800 cubic feet for the Gorgon tube

http://www.flickr.com/photos/erica_marshall/1792234104/

Surface area and volume of cones

in the following text you will

use the formula for the surface area of a cone

use the formula for the volume of a cone

cones are 3d figures that have a circule base, and a curved lateral surface.

the lateral surface that connects the base to a single point in the plane of the base is called the vertex

the altitude of a cone is the perpendicular segment from the vertex to the plane of the base.

the height of the cone is the length of the altitude

if the altitude of a cone intersects the base of the cone in the middle, the cone is a right cone. if it dosen't then it's an oblique cone.

the surface area of a right cone can be found by

for this equation, let the surface area = s, lateral area = l, base = b radius= r and slant height = h

s = l + b or s = π rh + π r²

the volume of a cone can be found by for this equation, let v = volume, r = radius, h = height and base = b

v = 1/3 bh or 1/3 π r²h

[|A link to better understand cones]

http://www.flickr.com/photos/detached/194216565/ Surface area and volume of spheres

in the following readings you will learn to

use the formula for the surface area of a sphere

use the formula for the volume of a sphere

a shere is the set fo all points in a space that are the same distance from a given point.

volume of a sphere =

v = 4/3 π r³

surface area of a sphere =

s = 4 π r²