(Solved): Task 3: Triple Integral A solid region \( E \) lies within the cylinder \( x^{2}+z^{2}=1 \), above ...

Task 3: Triple Integral A solid region \( E \) lies within the cylinder \( x^{2}+z^{2}=1 \), above the plane \( y+z=3 \) and below the cone \( y=5+x^{2}+z^{2} \). a) Draw the diagram using mathematical application (GeoGebra etc.) (3m) b) Draw the projection of diagram using mathematical application (GeoGebra etc.) \( (3 \mathrm{~m}) \) c) Hence, evaluate \( \iiint z^{2} d V \) using appropriate coordinate system. (12m)