Step 1 :

Conversion from rectangular to cylindrical co-ordinates :

$\"\"$

Conversion of integral from rectangular to cylindrical co-ordinates :

$\"\"$

Step 2 :

The solid is $\"\"$ .

The density function is $\"\"$ .

Substitute $\"\"$ in above equation. $\"\"$

The density function in cylindrical co-ordinates is $\"\"$ .

Find the z limits :

$\"\"$

Substitute $\"\"$ and $\"\"$ in above inequality.

$\"\"$

Find the r and $\"\"$ limits :

$\"\"$ is an equation of the circle with radius $\"\"$ .

Thus, $\"\"$ and $\"\"$ .

Step 3 :

Find the mass of the solid :

The mass is $\"\"$

Substitute the corresponding values in above equation.

$\"\"$

Solution :

The mass of the solid is $\"\"$ .