A solid E is the region between the parabolic surface z = y and the xy-plane...

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A solid E is the region between the parabolic surface z = y² and the xy-plane that is bounded by the planes x = 0, x= 1, y =-1 and y = 1. (1) Sketch the projections of solid E onto the three coordinate planes. (6 marks) In Cartesian coordinates, write a triple integral that gives the volume of solid E and compute it. (8 marks) Another solid G is the region that is bounded by the spherical surface a² + y² + z² = 9 and the cones ² = a² + y² and 32² = x² + y², for z > 0. Sketch the projections of solid G onto the three coordinate planes. (11) (6 marks) In spherical coordinates, write a triple integral that gives the volume of solid G and compute it. (12 marks) A solid E is the region between the parabolic surface z = y² and the xy-plane that is bounded by the planes x = 0, x= 1, y =-1 and y = 1. (1) Sketch the projections of solid E onto the three coordinate planes. (6 marks) In Cartesian coordinates, write a triple integral that gives the volume of solid E and compute it. (8 marks) Another solid G is the region that is bounded by the spherical surface a² + y² + z² = 9 and the cones ² = a² + y² and 32² = x² + y², for z > 0. Sketch the projections of solid G onto the three coordinate planes. (11) (6 marks) In spherical coordinates, write a triple integral that gives the volume of solid G and compute it. (12 marks)

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