SOLUTION: if the cost for materials to make a circular metal disk 3 cm in diameter is $.15, what would be the cost for materials to make a disk of the same thickness but 6 cm in diameter?

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Question 330573: if the cost for materials to make a circular metal disk 3 cm in diameter is $.15, what would be the cost for materials to make a disk of the same thickness but 6 cm in diameter?
would the answer be $.45? Thanks.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The assumption is that the cost of materials is based on the area of the disk (since the thickness is equivalent).
T=C%2AA, where T is total cost, C is cost per unit area, A is area.
The area of a circle is,
A1=%28pi%2F4%29%2AD%5E2=%28pi%2F4%29%2A3%5E2=%289%2F4%29%2Api
From the first example,
0.15=C%2A%289%2F4%29%2Api
C=0.15%2F%28%289%2F4%29%2Api%29
The area for the second disk is,
A2=%28pi%2F4%29%2A6%5E2=9pi
Since A2 is 4 times as much as A1, then the total cost will be 4 times as much.
T=%28%280.15%29%2F%28%289%2F4%29%2Api%29%29%2A%289%2Api%29=%280.15%29%284%29=0.60
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$0.60