SOLUTION: A clyinderical can of radius xcm has volume 144cm^3. the cost of producing the can is determined by it's surface area.
(A) show that the height of the can is h=144/piex^2.
(B
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Question 484460: A clyinderical can of radius xcm has volume 144cm^3. the cost of producing the can is determined by it's surface area.
(A) show that the height of the can is h=144/piex^2.
(B) find an expression for the surface area of the can
(C) find the dimensions that will minimise the cost of production.
All questions will help a lot, thanks!
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
A clyinderical can of radius xcm has volume 144cm^3. the cost of producing the can is determined by it's surface area.
(A) show that the height of the can is h=144/piex^2.
(B) find an expression for the surface area of the can
(C) find the dimensions that will minimise the cost of production.
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The volume of the can is V = where h = the height of the can
A) Solve for h in the above equation and substitute the value given for V:
B) The surface area of the can is given by
Substitute the expression for h derived in A) above:
C) The surface area will be a minimum where dS/dx = 0
Solve for x:
Multiply through by
The value for h can then be obtained from the expression derived in A).
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