Question

represent in cylindrical coordinates
in first octant
Q=(x,y,z): X^2+y^2<16 and y+z<4

Answer 1

\(x^2+y^2<16\), or \(-4<x<4\) and \(-4<y<4\), so you know that \(0<r<4\).

First octant, so you'll have \(0\le\theta\le\dfrac{\pi}{2}\).

\(y+z<4\), so by a simple conversion you have \(r\sin\theta+z<4\).

Answer 2

sweet!!! either we are both wrong or we are both right.