i am very stuck with this pls help...
Write a triple integral in cylindrical coordinates for hte volume of the solid cut from a sphere of radius 2 by a cylinder of radius 1, one of whose rulings is a diameter of the sphere. Take the axis of teh cylinder parallel to the z axis.
okay so i have the equation for the sphere to be x^2 + y^2 + z^2 =2 replacing x=rcos(theta) and y=rsin(theta) I get z=+/- sqrt.root.of [2-r^2], which I fancy are the limits for the z variable
its projection onto the r,theta plane gives r<=cos(2theta) so I fancy that the limits for the r variable are 0 to cos(2theta)
and the limits for the theta variable from -pi/2 to pi/2
the problem is i am wrong, because the back of the book gives the mass of the solid to be "9,56 times the uniform density ro"
but I don't get as the volume 9,56
please help me