Volume figure determined by surfaces.

Question

Figure is determined by the following surfaces. Calculate the volume.

$$ 1 = (x-1)^2 + y ^2 (z \ge 0 )$$ $$ z = -(x^2 + y^2 ) +5$$ $$x^2 + y^2 = 4z^2 $$

Please help me with that.

Answer 1

Hint: The body is inside the cylinder $(x-1)^2+y^2\leq 1$ and below it is bounded by $z=\frac{1}{2}\sqrt{x^2+y^2}$ and above by $z=5-(x^2+y^2)$.