what should be the dimensions of the cylinder if you wanted it to have the least amout of surface area as possible?

Question

the cylinders volume is 100ft cubed

Answer 1

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.

Answer 2

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

Answer 3

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.

Answer 4

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????

Answer 5

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.

Answer 6

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

Answer 7

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

Answer 8

what ends?

Answer 9

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