# Surface Integrals – On a cone – Exercise 4068

Exercise

Calculate the integral

$$\int\int_S (x^2+y^2+z^2) ds$$

Where S is part of the cone

$$z=\sqrt{x^2+y^2}$$

That is on the circle

$$x^2+y^2\leq 2x$$

$$\int\int_S (x^2+y^2+z^2) ds=3\sqrt{2}\pi$$