[See Steps] Find the volume inside the paraboloid z=x^2+y^2 below the plane
Question: Find the volume inside the paraboloid \[z={{x}^{2}}+{{y}^{2}}\] below the plane \[z=4\] .
Deliverable: Word Document 
![[All Steps] Sketch the region R and](/images/solutions/MC-solution-library-50554.jpg "[All Steps] Sketch the region R and evaluate the double integral:")
[All Steps] Sketch the region R and evaluate the double integral:
(All Steps) Evaluate ∫_0^1∫_0^√1-x^2e^-(x^2+y^2)dydx
![[See Steps] Use polar coordinates to calculate](/images/solutions/MC-solution-library-50556.jpg "[See Steps] Use polar coordinates to calculate the area of the")
[See Steps] Use polar coordinates to calculate the area of the
Solution: A lamina has the shape of a closed region bounded by
![[Steps Shown] Find the center of mass](/images/solutions/MC-solution-library-50558.jpg "[Steps Shown] Find the center of mass of the lamina bounded by")
[Steps Shown] Find the center of mass of the lamina bounded by
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