Answer
$200 \text{ ft}^3$
Note that this is an approximation rounded to the nearest hundred.
Work Step by Step
Convert by multiplying $\dfrac{1 \text{ ft}^3}{7.48 \text{ gal}}$ to obtain:
$\require{cancel}
z=1496 \cancel{\text{ gal}} \cdot \dfrac{1\text{ ft}^3}{7.48 \cancel{\text{ gal}}}
\\=\dfrac{1496}{7.48} \text{ ft}^3
\\=200 \text{ ft}^3$