let V be the solid region such that x^2 + y^2 + z^2

Question

let V be the solid region such that x^2 + y^2 + z^2 <= 9, x^2 + y^2 <= 4, x <= 0,  z >= 1.

a) sketch the region V and describe it in cylindrical coordinates.
b)if the mass density per unit volume of V is given by rho(x,y,z) = 5(y+2)z, use cylindrical coordinates to find the mass V

I'm so lost, is someone able to help me? haha 
thanks!

anonymous · Answer

$x^2+y^2+z^2\le9$ gives you all the points inside a sphere of radius 3.

$x^2+y^2\le 4$ gives you all the points inside a circle on the $x-y$ plane with radius 2.

$x\le0$ and $z\ge 1$ are some added restrictions. I'll try to draw all this:
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