Chapter 14.6, Problem 23ES

Determine whether the statement is true or false. Explain your answer.

Let G be the solid region in 3-space between the spheres of radius 1 and 3 centered at the origin and above the cone $z=\sqrt{x^2+y^2}.$ The volume of G equals ${\displaystyle {\int }_0^{\pi /4}{\displaystyle {\int }_0^{2\pi }{\displaystyle {\int }_1^3{\rho }^2\sin \varphi d\rho d\theta d\varphi }}}$