No, you need to divide by $\displaystyle 12^3$...essentially a 12 for each of the 3 spatial dimensions.
$\displaystyle 7128\text{ in}^3\cdot\left(\frac{1\text{ ft}}{12\text{ in}} \right)^3=\frac{7128}{12^3}\,\text{ft}^3=156.75 \text{ ft}^3$
No, you need to divide by $\displaystyle 12^3$...essentially a 12 for each of the 3 spatial dimensions.
$\displaystyle 7128\text{ in}^3\cdot\left(\frac{1\text{ ft}}{12\text{ in}} \right)^3=\frac{7128}{12^3}\,\text{ft}^3=156.75 \text{ ft}^3$
An impatient person has no business trying to help on a forum. You are doing fine.
Yes, that is the correct answer. Now, in order to find this area using integration, I recommend orienting your coordinate axes such that the origin is at the bottom corner under the lowest point of the ceiling. We will then want to write the upper slanting edge of the wall as a linear function. What would the y-intercept and the slope be?