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# A group of engineers is building a parabolic satellite dish whose shape will be formed by rotating the curve $y = ax^2$ about the y-axis. If the dish is to have a 10-ft diameter and a maximum depth of 2 ft, find the value of $a$ and the surface area of the dish.

## $$a=\frac{2}{25} \quad 90.01 \mathrm{ft}^{2}$$

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Applications of Integration

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