Answer:
[tex]mass=108\sqrt{2\pi }[/tex]
Step-by-step explanation:
First
[tex]\frac{dz}{dx}=\frac{x}{\sqrt{x^{2}+y^{2} } }[/tex]
And
[tex]\frac{dz}{dy}=\frac{y}{\sqrt{x^{2} +y^{2} } } \\m=\int\limits^{} \int\limits^{}_s {(10-z)} \, ds\\ m=\sqrt{2}\int\limits^{ } \int\limits^{}_{D} {(10-\sqrt{(x^{2}+y^{2} } )} \, dA \\m=\sqrt{2}\int\limits^{2\pi }_{0}{ } \int\limits^{4}_{1} {(10-r)} \, rdrdO\\ m=2\sqrt{2\pi } \int\limits^{4}_{1} {(10r-r^{2} )} \, dr\\ m=108\sqrt{2\pi }[/tex]
