Question
A satellite-signal receiving dish is formed by revolving the parabola given by $x^{2}=20 y$ about the $y$ -axis. The radius of the dish is $r$ feet. Verify that the surface area of the dish is given by $2 \pi \int_{0}^{r} x \sqrt{1+\left(\frac{x}{10}\right)^{2}} d x=\frac{\pi}{15}\left[\left(100+r^{2}\right)^{3 / 2}-1000\right]$
Step 1
First, we need to find the equation of the parabola in terms of $y$. Since we are given $x^2 = 20y$, we can solve for $y$ to get $y = \frac{x^2}{20}$. Show more…
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