Cylindrical coordinates clearly and detailed notes... | Filo

SOLVED:(a) Write a triple integral in cylindrical coordinates for the volume of the solid cut from a ball of radius 2 by a cylinder of radius 1, one of whose rulings is a diameter of the ball. Hint: Take the axis of the cylinder parallel to the z axis; a cross section of the cylinder then looks like the figure in Problem 2 . (b) Write a triple integral for the moment of inertia about the z axis of a uniform solid occupying this volume. (c) Evaluate the integrals in (a) and (b), and find I as a m