Posted by Mackenzie on .
what should be the dimensions of the cylinder if you wanted it to have the least amout of surface area as possible?
the cylinders volume is 100ft cubed

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bobpursley,
I assume this is calculus class.
Volume= PI*radius^2*h
h= volume/(PI*radius^2)
Surface=PI*radius^2*2 + PI*radius*height
Surface= PI*radius^2 * 2 + PI*radius*volume/(PI*radius^2)
Take the derivative of surface with respect to radius, set it to zero, and solve for radius. 
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Mackenzie,
i am only in 7th grade! Could you explain that a little more to me

math 
bobpursley,
Sorry, this question is a typical college level calculus question. For a seventh grader, it is a little harder.
Try this. Graph Surface area vs radius according to the equation I gave you...
Surface= 2*PI*radius^2 + 100/radius
You will see a graph that has a minimum. If you have a graphing calculator, it is easy to graph.
Once you have the minimum, read the radius point on the curve. Then,
Height= 100/(PI*radius^2)
This problem is a bit advanced for a seventh grader. 
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Mackenzie,
i have an answer but i don't know if it is right! will you tell me if i am right or wrong.
i got that the dimensions 31.83098862 ft by 2 ft would have the least surface area for the problem.
am i right or wrong?
can you help me???? 
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bobpursley,
I don't get that. I get the diameter to be 5.84 feet (twice the cube root of 25).
You can figure the height . I get less than four feet.
check me. 
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Mackenzie,
how did you figure that out?
this is what i did!
100 divided by pie and i got 31.83098862 ft and then that multiplied by 2 is 100!
please help me 
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bobpursley,
One note. I included the ends in the surface area. If they are not to be included, then it is a different answer.

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Mackenzie,
what ends?

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Mackenzie,
please help! explain it to me in a 7th grade way! i am taking pre algebra