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!

Answer 1

\(x^2+y^2+z^2\le9\) 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: