1. The volume of the solid of revolution obtained by rotating the closed figure formed by the function $y=\sqrt{b^{2}-\frac{b^{2} x^{2}}{a^{2}}}$ and the $x$-axis around the $y$-axis once is $\qquad$ .
(Tip: Similar to the derivation of the volume of a sphere, according to Zu's principle, the volume of this solid of revolution can be regarded as the volume of a cylinder (base radius $a$, height $b$) minus a cone (base radius $a$, height $b$). Answer: $\frac{2}{3} \pi a^{2} b$.)