33e2f0…: “Along a still butterfly”

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Let $F(x,y) = x^2+y^2+10$ and let $D = \{(x,y): x^2+y^2\le 16\}$ . Set-up an iterated integral that computes the surface area of the surface $z=F(x,y)$ over $D$ . $\iint _D \d S = \int _{\answer {0}}^{\answer {2\pi }} \int _{\answer {0}}^{\answer {4}} \answer {\sqrt {1+4r^2}r}\d r \d \theta$

Compute the iterated integral above. $\iint _R \d S = \answer {\frac {1}{6} \left (65 \sqrt {65}-1\right ) \pi }$