Question

the sum of the height and diameter of a cylinder is 24 cm. what is the maximal volume of the cylinder?

Answer 1

\[ 512 \pi \space cm^3\]

Answer 2

please could u tell me how u got the answer?

Answer 3

Am I correct?

Answer 4

i dont know

Answer 5

A Mathematica PDF solution with comments is attached.

Answer 6

@robtobey:Nice but don't you think it's a bit overkill for considering the problem?:

Answer 7

Also,you have explain why r=8 gives the maximum solution either geometrically or intuitively.

Answer 8

Out[9] is the derivative of the cylinder volume with respect to r. Out[10] is the two solutions for r obtained by setting the derivative to zero and solving for r, a standard calculus method for obtaining the maximum cylinder volume in this case. In Mathematica the r solutions are given as replacement rules, r -> 8, rather than the traditional r = 8.

Your's and my responses are probably the most extreme problem solution forms presented on this site. Yours is in this case the answer only followed by an ignored request, at least so far, from the problem poser, yahya__vip, asking how you obtained the 512pi answer, vs mine, which includes narrative, the math solution procedure and a high quality cylinder volume function plot. By the way, the plot allows one to guess a solution value and is not presented as a proof of the solution.

Answer 9

ty alot for the help but i dont think that is the answer,the lesson is about derivatives btw

Answer 10

@ yahya__vip

Putting aside the this and that between myself and FoolForMath, both of us agree that the maximum volume of the cylinder where the sum of the cylinder's diameter and height is restricted to 24 cm is:\[512 \pi \text{ cm}^3 \]If you don't agree can you prove otherwise?

Answer 11

well,if you can plot the graph the solution is just intuitively plausible in this case.

Answer 12

what I don't like is user wants to know "how" and not "why",how is easy but doesn't makes sense if you don't know why...