A torus is formed when a circle of radius 2 centered at (3,0) is revolved about the y-axis. a. Use the shell method to write an integral for the volume of the torus. b. Use the washer method to write an integral for the volume of the torus. c. Find the volume of the torus by evaluating one of the two integrals obtained in parts (a) and (b). (Hint: Both integrals can be evaluated without using the Fundamental Theorem of Calculus.)

2. A circular cylindrical hole is bored through a solid sphere, the axis of the hole is being a diameter of the sphere. If the volume of the remaining solid portion of the sphere is V = 2π 2 1th LV LAVE rdrdzde, then a) find the radius of the hole and the radius of the sphere, b) evaluate the integral.

Choose the correct awnser. Find the volume of the solid whose base is the region enclosed by the semi-circle y=(1-x^2)^1/2 and the x-axis, and whose cross-sections perpendicular to the x-axis, and whose cross-sections perpendicular to the x-axis are squares.  a) 3/2  b) 5/4  c) 6/5  d) 4/3  e) pi/2  f) 1