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Expert: Alon Mandes - 1/21/2011


Question
A rectanglular shet of metal of perimeter 36cm and dimensions x and y is to be rolled into a cylinder.(Volume of

cylinder is V = pi.r^2h) What values of x and y give the largest volume?

Answer
Perimeter of the rectanglular is : 2x+2y . Thus , 2x+2y=36 --> y=18-x .
Hiegth of the cylinder , H=y .
Radius of the cylinder r : 2πr=x --> r=x/(2π) .
Thus,
Volume of the cylinder : V=πr²h=π[x/(2π)]²y=π[x/(2π)]²(18-x)=[1/(4π)]*[x²(18-x)]
V=[1/(4π)]*[18x²-x³)] .
To find maximum , we derive V with respect to x , & solve : V'(x)=0 ..
So,
V'(x)=[1/(4π)]*[36x-3x²)]
V'(x)=0 --> 36x-3x²=0 --> 12x-x²=0 --> 12-x=0 --> x=12 cm .
Let's calculate y :
y=18-x=18-12=6 cm .

Alon.

Calculus

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Alon Mandes

Expertise

Kind of questions I can answer : Limits, Derivatives, Integration, Implicit functions, continuousity, differentiation ,Extremum problems, Lagrange multipliers, Gradients, Surface integrals, Multi variables functions ,Multi variables Integrals,Complex variables ,Complex functions, Curves, Trajectory integrals & Vector analyse,Divergence,Rotor & word problems. Kind of question I can't answer : Economics,Combinatorics,infinite series & convergence ,Statistics & Probabilities .

Experience

1. I'm a team member of mathnerds (math site for answering questions) 2. I'm a team member in the Student's Union of the Technion, helping students who have problems in mathematics. 3. 2 years of experience as a math teacher in college. 4. I give free homework help for high school students in Mathematics & Physics. 5. I teach part time in collage the subjects : "Digital Signal Processing" , "Random Signals & Noise" , "Complex Functions".

Organizations
Hi-Tech company : GSM4VOIP ; job possition : Algorythm developer.

Education/Credentials
M.A in Mathematics & Bs.c in Electronics.

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