Re: Optimum volume and surface area Q!uestion need help ASAP  TOPIC_SOLVED

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Re: Optimum volume and surface area Q!uestion need help ASAP

Postby hopelessatmath071986 on Wed Jul 08, 2009 11:38 pm

Hey i got a question im doing a test tomororw on surface areas and volumes of various shapes and geometric shapes .
The question is from MAP4c1 text book basically its ona ahnd out which the question is on a review for chapter 1.1.6 Analyse Optimum Volume and Surface Area pages 54-63
As ive been taught the formula for figuyring out volume and surface area for a cylinder is 2 pie r squared + 2 pie r height for the surface area. and then for the volume equals pie r squared times height..
When there is unknown characters say for instance the radius but you hve the height and you need too figure out what the radius is and you have the volume what ive been taught is too use the formula Volume = pie times radius but you dont know what r is.. soo its like an x. unknown. times the height
soo say the volume was 1500 cm cubed
and the height was 38 cm. but your solving for the radius
I would plug in 1500= 3.14 times r times 38
then 1500 = 119.32 R
1500 would be divided by 119.32 and the other side has too do the same thing soo it would be divided by it self isolating the r..
which would now be 1500 divided by 119.32 leaving the R too equal 12.57 whcih would still need too be found because its still squared.. soo the square root of 12.57 w0uld be 3.54 soo therefore r would be 3.55 after rounded. That was too solve for r

the opppositie if only the height was involved would incorportate the formula volume erquals pie times radius times the unkown h but.. tghe question im having problems with doesnt give you the radius nor does it give you the hieght.. only the volume is given.. theres nothing given.. too plug into either equation..


A cydrical juice container is to have a volume of 2l or 2000 cm cubed. Determine the dimensions of the container with minmum surface area and suggest two reasons why the manufaturer womay not choose this design. Im unsure how too answser it without measuring it or having given variable. pleaseeeee help ..
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Postby stapel_eliz on Sat Jul 11, 2009 6:34 pm

hopelessatmath071986 wrote:A cydrical juice container is to have a volume of 2l or 2000 cm cubed. Determine the dimensions of the container with minmum surface area and suggest two reasons why the manufaturer womay not choose this design.

Write down the formula for the volume "V" of a right circular cylinder with radius "r" and height "h". Plug "2000" in for "V", and solve for "h" in terms of "r".

Write down the formula for the surface area "SA" of the cylinder, and replace "h" with the expression you obtained. Simplify to get "SA" in terms only of "r".

Use whatever methods you have been taught to minimize the value of "SA". Once you have found the mathematically-optimal solution, look at the figure that results, and think about ergonomics. Would the average shopper want to deal with a can in that shape? Etc.
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