Question 208204: how did they find the surface area ???
of cube,cone,cylinder,square,rectangle,rec.prism and so on....????
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! there are formulas for each.
most of the time you can just look at the solid and count the number of surfaces.
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cube has 6 surfaches, each of which is a square.
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cone has 2 surfaces. the base is a circle, and the side looks much like a triangle once you cut it lengthwise and flatten it out.
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a cylinder has 2 circles on each end the the tube looks like a rectangle once you cut it length wise along the tube and flatten it out.
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it's a matter of visualization of what the flattended figure looks like.
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if you've made shapes with pieces of paper before than you get the idea of how these shapes are formed.
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here's a website that discusses the subject:
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http://www.utexas.edu/student/utlc/learning_resources/math_handouts/surface_area_solids.pdf
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here's a website on a sphere and other objects. just follow the pages to get all that she has:
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http://math.about.com/od/formulas/ss/surfaceareavol.htm
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next page is a cone from the last website address.
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page after that is a cylinder.
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page after that is a rectangular prism.
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page after that is a square based pyramid.
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page after that is an isosceles triangle based prism.
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for some reason other she didn't include a triangular pyramid. this would be a pyramid with a triangular base. it is formed by 3 triangles as sides and one triangle as base.
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this website has the volume of a triangular pyramid at the bottom of the page.
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http://www.mathsteacher.com.au/year10/ch14_measurement/25_pyramid/21pyramid.htm
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here's a website that has all sorts of useful geometric formulas, including solids.
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http://www.analyzemath.com/Geometry/formulas/table_formulas_geometry.html
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if you need help on the surface area of a particular object, just go to www.yahoo.com or www.google.com and do a search on that figure.
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an example would be:
surface area of a pentagon solid
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here's a neat website that shows how some of the solids are formed.
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http://www.mathsnet.net/geometry/solid/nets.html
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it's mostly logic, visualization, and a thought process that takes sections and puts them together to form the solid.
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with somne solids, the use of calculus is definitely used.
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calculus takes the limit of something as the length or width of it approaches zero, or the number of sections approaches infinity. this is used to calculate the surface area of the volume of many solids that don't fit into a neat pattern such as a cube or a rectangular solid.
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to get the volume of a sphere, calculus is helpful and was more then likely used to generate the final formula that you use.
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similarly with the cylinder. it's the area of the circle times the height. that's equivalent to stacking up lots of skinny little circles much like you would stack up a cylinder of coins.
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a lot of them use the area of the base times the height times a factor. for instance, the area of a triangle is 1/2 base times height.
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for example:
volume of a pyramid is proved by calculus as explained in the following website:
http://en.wikipedia.org/wiki/Pyramid_%28geometry%29
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there's tons of information on the internet is you take the time to look.
enjoy.
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