Asked by Mackenzie

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
Answered by 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.
Answered by Mackenzie
i am only in 7th grade! Could you explain that a little more to me
Answered by 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.
Answered by 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????
Answered by 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.
Answered by 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
Answered by bobpursley
One note. I included the ends in the surface area. If they are not to be included, then it is a different answer.
Answered by Mackenzie
what ends?
Answered by Mackenzie
please help! explain it to me in a 7th grade way! i am taking pre algebra
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