Finding the height and top radius of cone so that volume is maximum and Finding the angle so that the volume is maximum

You have a 6-inch diameter circle of paper which you want to form into a drinking cup by removing a pie-shaped wedge with central angle theta and forming the remaining paper into a cone. - You are given that 3 is the slant height

a) Find the height and top radius of the cone so that the volume of the cup is as large as possible.

b) What is the angle theta of the arc of the paper that is cut out to create the cone of maximum volume?

I know how to do related rates with volume, but I can't seem to figure it out with angles being cut out from a circle.

You have a 6-inch diameter circle of paper which you want to form into a drinking cup by removing a pie-shaped wedge with central angle theta and forming the remaining paper into a cone. - You are given that 3 is the slant height

a) Find the height and top radius of the cone so that the volume of the cup is as large as possible.

b) What is the angle theta of the arc of the paper that is cut out to create the cone of maximum volume?

I know how to do related rates with volume, but I can't seem to figure it out with angles being cut out from a circle.