Answer
$V$ = $\frac{4}{3}\pi{a^3}$
Work Step by Step
$x^2+y^2+z^2=a^2$
$z$ = $±(a^2-r^2)$
$V$ = $2\int_0^{2\pi}\int_0^a{\sqrt {a^2-r^2}}rdrdθ$
use substitution integration
$u$ = $a^2-r^2$
$du$ = $-2rdr$
$-\frac{1}{2}du$ = $dr$
$V$ = $-\frac{2}{3}\int_0^{2\pi}[a^2-r^2]^{\frac{3}{2}}|_0^adθ$
$V$ = $-\frac{2a^3}{3}\int_0^{2\pi}1dθ$
$V$ = $-\frac{2a^3}{3}[θ]_0^{2\pi}$
$V$ = $\frac{4}{3}\pi{a^3}$
