# Spherical and Cylindrical Coordinates – On a cone – Exercise 4617

Exercise

Calculate the integral

$$\int\int\int_T z\sqrt{x^2+y^2} dxdydz$$

Where T is bounded by the surfaces

$$x^2+y^2\leq 2x, y\geq 0, z\geq 0, z\leq 3$$

$$\int\int\int_T z\sqrt{x^2+y^2} dxdydz=8$$