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Multivariable Calculus

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Moderate

Paraboloid and Cone

MVCALC-GUYJL0

Find the surface area of the shape bounded by paraboloid $x^2+y^2=z$ and cone $z=2-\sqrt{x^2+y^2}$.

A

$\cfrac{\pi(6\sqrt{2}+5\sqrt{5}-1)}{6}$

B

$\cfrac{\pi(\sqrt{2}+\sqrt{5}-1)}{6}$

C

$\cfrac{\pi(\sqrt{5}-1)}{3}$

D

$\cfrac{\pi(\sqrt{2}-1)}{3}$

E

None of the above