Volume of the solidUsing geometry, calculate the volume of the solid under z = 49 − x 2 − y 2 and over the circular disk x 2 + y 2 ≤ 49.I am really confused for finding the limits of integration. Any help?

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Volume of the solidUsing geometry, calculate the volume of the solid under   z  =      49    −          x      2        −          y      2       and over the circular disk       x    2    +      y    2    ≤  49.I am really confused for finding the limits of integration. Any help?

Deanna Sweeney · Accepted Answer

Step 1If you are using double integration, by considering an elementary area dxdy  on the X-Y plane, the elementary volume (dV) of solid can be given as   d  V  =  z  d  x  d  y  V  =  ∬  z  d  x  d  yStep 2Since the surface   z  =      49    −          x      2        −          y      2          intersecting the disk       x    2    +      y    2    ≤  49    in the XY plane hence the limits can be applied as follows  V  =      ∫          −      7        7        ∫          −              49        −                  y          2                                    49        −                  y          2                          49    −          x      2        −          y      2        d  x  d  yFurther, I guess that you can change the order of integration for simplification

Using geometry, calculate the volume of the solid under z=sqrt{49-x^2-y^2} and over the circular disk x^2+y^2 leq 49.

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