#### Answer

$562.9 \ ft^3$

#### Work Step by Step

Apply the Pythagorean formula to determine the height of the pyramid.
$h^2=l^2-(\dfrac{r}{2})^2 \implies h^2=(15)^2 -(5.5)^2\implies h=13.95 \ m$
The volume of a square pyramid is:
$Volume =\dfrac{1}{3} \times b\times h=\dfrac{1}{3} \times S^2 \times h$
Plug the values of $S$ and $h$ into the formula to obtain:
$Volume=\dfrac{1}{3} \times (11)^2 \times (13.95)\\ =\dfrac{1}{3} \times 121 \times 13.95 \\=562.9 \ ft^3$