Posted by **Mackenzie** on Monday, February 4, 2008 at 8:03pm.

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**, Monday, February 4, 2008 at 8:06pm
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**, Monday, February 4, 2008 at 8:08pm
i am only in 7th grade! Could you explain that a little more to me

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**bobpursley**, Monday, February 4, 2008 at 8:13pm
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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**bobpursley**, Monday, February 4, 2008 at 8:27pm
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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**bobpursley**, Monday, February 4, 2008 at 8:31pm
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**, Monday, February 4, 2008 at 8:33pm
what ends?

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