Question 1 a). In an engineering lab, a cap was cut from a solid ball of radius 2 meters by a plane 1 meter from the center of the sphere. Assume G be the smaller cap, express and evaluate the volume of G as an iterated triple integral in: [Verify using Mathematica] i). Spherical coordinates. ii). Cylindrical coordinates. iii). Rectangular coordinates. [7+7+ 6 =20 marks] b). Using an appropriate triple integral, evaluate the volume of: [Verify using Mathematica] 1 ) . 11 ) . N z = 3VI -x2 - v2 Z= VI-x- - - 12 r = sin 0 r = cos 0 Figure 1 Figure 2 [5 + 5 = 10marks]