area and cost

**rusu147** · August 5th 2010, 08:12 PM

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?

**eumyang** · August 5th 2010, 08:26 PM

I'm going to assume that this plate is donut-shaped. Let $R = 12\,in$ and $r = 5\,in$ . The area of this plate would be
$\begin{aligned} A &= \pi R^2 - \pi r^2 \\ &= 12^2 \pi - 5^2 \pi \\ &= 144 \pi - 25 \pi \\ &= 119 \pi \\ &\approx 373.85\,in^2 \\ \end{aligned}$

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

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