You are designing a 1000 right circular cylindrical can whose manufacturer will

Question

You are designing a 1000    right circular cylindrical can whose manufacturer will take waste into account. There is no waste in cutting the aluminum for the side, but the top and bottom of radius r will be cut from squares that measure 2r units on a side. The total amount of aluminum used up by the can will therefore be

                                    A=8r^2+2(pi)rh                

Find the radius of the most economical can. Just find the critical point, this will be the radius of the most economical can. Don

Explanation / Answer

we have pi*r^2*h=1000(volume)

thus A=8r^2+2(pi)r*1000/pi*r^2=8r^2+2000/r

for radius of the most economical cylinder, dA/dr=0

16r-2000/r^2=0

=>r^3=1000/8

=>r=10/2=5

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.