Asked by Matelita
A cylindrical container is to be produced that will have a capacity of 10 metre cubic
. The top and the
bottom of the container are to be made of material costing $2.00 per square meter, while the
side of the container is to be made of material costing $1.50 per square meter. Find the
dimensions that will minimize the total cost of the container.
. The top and the
bottom of the container are to be made of material costing $2.00 per square meter, while the
side of the container is to be made of material costing $1.50 per square meter. Find the
dimensions that will minimize the total cost of the container.
Answers
Answered by
Reiny
radius of cylinder ---- r
height of cylinger ---- h
volume = πr^2 h = 10
h = 10/(πr^2)
cost = 2(2πr^2) + 1.5(2πrh) <------ 2 circles plus a rectangle
= 4πr^2 + 3πr(10/(πr^2))
= 4πr^2 + 30/r
d(cost)/dr = 8πr - 30/r^2 = 0 for a min of SA
8πr = 30/r^2
r^3 = 15/(4π)
r = .... , for a minimum cost
now that you have r, go back and find h
height of cylinger ---- h
volume = πr^2 h = 10
h = 10/(πr^2)
cost = 2(2πr^2) + 1.5(2πrh) <------ 2 circles plus a rectangle
= 4πr^2 + 3πr(10/(πr^2))
= 4πr^2 + 30/r
d(cost)/dr = 8πr - 30/r^2 = 0 for a min of SA
8πr = 30/r^2
r^3 = 15/(4π)
r = .... , for a minimum cost
now that you have r, go back and find h
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