Question

Use cylindrical coordinates to find the mass of the solid Q.

Answer 1

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 .