MathDB

In the

xyz

space, consider a right circular cylinder with radius of base 2, altitude 4 such that

\left\{ \begin{array}{ll} x^2+y^2\leq 4 &&emsp; \\ 0\leq z\leq 4 &&emsp; \end{array} \right.

Let

V

be the solid formed by the points

(x,\ y,\ z)

in the circular cylinder satisfying

\left\{ \begin{array}{ll} z\leq (x-2)^2 &&emsp; \\ z\leq y^2 &&emsp; \end{array} \right.

Find the volume of the solid

V

706