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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

  • math -

    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.

  • math -

    i am only in 7th grade! Could you explain that a little more to me

  • math -

    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.

  • math -

    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????

  • math -

    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.

  • math -

    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

  • math -

    One note. I included the ends in the surface area. If they are not to be included, then it is a different answer.

  • math -

    what ends?

  • math -

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

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