SOLUTION: calculate the volume of an ingot 40x50x400 mm long. it is cast into a cylinder 210mm diamter, calculate the lenght and surface area of this cylinder?

Question 243171: calculate the volume of an ingot 40x50x400 mm long. it is cast into a cylinder 210mm diamter, calculate the lenght and surface area of this cylinder?
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
Setup your variables:
length = l = 40
height = h = 50
depth = d - 400
Volume of Ingot = length * height * depth
V = 40 * 50 * 400 = 2000 * 400 = 800,000
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Hint: As soon as I saw this big numbers, I started an Excel workbook to do my calculating. If you have a calculator, now would be a good time to go get it.
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The volume of whatever is shaped into the ingot is to be cast into a cylinder 210 in diameter.
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We know several more useful facts:
Volume of cylinder = area of base * height
Area = pi* radius^2
Radius = diameter/2 = 210/2 = 105
Area = pi * 105^2
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So our unknown is the height of the cylinder.
But we know it has to have volume 800,000 to hold the same volume as the ingot.
800,000 = pi* 105^2 * height of cylinder
Solving for the height, we find:
ht = 23.097316
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We can check our work by recomputing the volume and comparing it to the given volume.
Does pi*(105^2)*23.097316 = 800,000? Yes.
The height of the cylinder will be 23.097316 to have volume equal to an ingot 40 by 50 by 400.
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Are we done yet?
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Well, checking back to the question, we also are asked the surface are of the cylinder.
That is simply the circumference * ht of the cylinder.
ht = 23.097316
Circumference is just pi * diameter
C = pi * 210
C = 659.7344573
Surface area = C * ht
S = 659.7344573 * 23.097316
S = 15238.09524
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Now we're done.
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