$y^2 + 1^2 = 2^2$
$y = \sqrt{3} ~ \text{ft}$
$h^2 + \left( \frac{2}{3}y \right)^2 = 2^2$
$h^2 + \left( \frac{2}{3}\sqrt{3} \right)^2 = 2^2$
$h = \sqrt{8/3} ~ \text{ft}$
Note that the base area is an equilateral triangle
$V = \frac{1}{3}A_b h$
$V = \frac{1}{3} \left[ \frac{1}{2}(2^2)\sin 60^\circ \right]\sqrt{\frac{8}{3}}$
$V = 0.9428 ~ \text{ft}^3$ ← answer