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Thread: area and cost

  1. #1
    Aug 2010

    area and cost

    An aluminum plate is made according to the following dimensions. THe outer radius is 12 inches and the inner radius is 5 insches. Use Pi = 3.14 as an approximate value. (a) Hamy square inches in area is the aluminum plate? (b) If the cost to construct the plate is 5.50 per square inch, what is the construction cost?
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  2. #2
    Senior Member eumyang's Avatar
    Jan 2010
    I'm going to assume that this plate is donut-shaped. Let $\displaystyle R = 12\,in$ and $\displaystyle r = 5\,in$. The area of this plate would be
    $\displaystyle \begin{aligned}
    A &= \pi R^2 - \pi r^2 \\
    &= 12^2 \pi - 5^2 \pi \\
    &= 144 \pi - 25 \pi \\
    &= 119 \pi \\
    &\approx 373.85\,in^2 \\

    Multiply this amount by $5.50/sq. in. to get the cost.
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