and above by the sphere
Step 1
To set the triple integral in cylindrical coordinates
By using relation,
Thus,
The cone
And the sphere become
To find the limit of r,
Consider,
Step 2
Thus, we can describe the region as
Hence, the triple integral for the volume by cylindrical coordinates is
Step 3
Now, to set the triple integral in spherical coordinates
Since,
The sphere
From the cone
Step 4
Thus, we can describe the region as
Hence, the triple integral for the volume of the solid by spherical coordinate is
Step 5
Now, evaluating the integral of cylindrical coordinate we get.
And evaluating the integral of spherical coordinate
Thus, by both coordinate systems, we get the same volume.
Therefore, both triple integrals are appropriate.
Below are various vectors in cartesian, cylindrical and spherical coordinates. Express the given vectors in two other coordinate systems outside the coordinate system in which they are expressed
Descibe in words the region of