034 Review Problem - Sphere dropped into a cone

$\theta = 16.56^\circ$
 

$y = \dfrac{r}{\sin \theta} = \dfrac{1.249}{\sin 16.56^\circ}$

$y = 4.382 ~ \text{in.}$
 

$5.016 - h = y - r$

$5.016 - h = 4.382 - 1.249$

$h = 1.883 ~ \text{in.}$
 

Amount of water that overflows
$V = \text{segment of a sphere}$

$V = \frac{1}{3}\pi h^2(3r - h) = \frac{1}{3}\pi(1.883^2)[ \, 3(1.249) - 1.883 \, ]$

$V = 6.92 ~ \text{in.}^3$           answer