a) Use double integrals to find the volume of the solid lying under the surface

z = 1+x+y and above the region in the xy-plane bounded by x = y² and .x = 4.

b) Find the mass of the region bounded by the curve r = 2 sin given that the density

across the region is constant.

c) An ice cream cone can be described as being a solid bounded below by the cone

==√√3(x² + y²) and above by the hemisphere .x² + y² +2²=1, z 20.

The volume of such a cone (ice cream and cone combined) can be calculated using

triple integrals.

(i) Set up the triple integral in rectangular co-ordinates to calculate the volume.

(ii) Set up this triple integral in cylindrical co-ordinates to calculate the volume.

(iii) Set up this triple integral in spherical co-ordinates to calculate the volume. (It

may be helpful to know that the cone makes an angle of with the z axis.)

(iv)Calculate the volume of this ice cream cone.