I'm trying to solve a calculus problem, I need to find the mass of a cylinder, I'm close to the answer, I got $8\pi$ but it should be $16\pi$.
I think my mistake lies in the density function since it uses some linear algebra (?) ideas.
"The density at the point $(a,b,c)$ equals double of the distance of the point to the plane $z=0$"
At first I did $\sqrt{a^2+b^2}$ but that's the distance of a point to the $z$-axis not $z$-plane right?
If we want to find the distance of a point $(a,b,c)$ to the $z$-plane can we just lower this point until it reaches the $z$-plane? So we have the distance between $(a,b,c)$ and $(a,b,0)$? So we get $\sqrt{z^2}=z$
As people corrected in the comments the distance of the point (a,b,c) to the z-plane is the distance of this point (a,b,c) to the point (a,b,0) which is: $|c|$.
I managed to calculate the mass of the solid correctly and my question is solved.