Composite solid made of a rectangular prism and a cylinder.

To find the total volume of the figure, we need to calculate the volume of the rectangular prism (the bottom box) and the volume of the cylinder (the top part) separately, then add them together.

Step 1: Calculate the volume of the rectangular prism.
The formula for the volume of a rectangular prism is:
$$ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} $$

From the diagram:
* Length = $14\text{ ft}$
* Width = $8\text{ ft}$
* Height = $12\text{ ft}$

Calculation:
$$ 14 \times 8 \times 12 $$
$$ 14 \times 8 = 112 $$
$$ 112 \times 12 = 1344 $$

So, the volume of the rectangular prism is $1344\text{ cubic feet}$.

Step 2: Calculate the volume of the cylinder.
The formula for the volume of a cylinder is:
$$ \text{Volume} = \pi \times r^2 \times h $$
*(We will use $3.14$ for $\pi$)*

From the diagram:
* Radius ($r$) = $4\text{ ft}$
* Height ($h$) = $8\text{ ft}$

Calculation:
First, square the radius:
$$ 4^2 = 4 \times 4 = 16 $$

Next, multiply by the height and $\pi$:
$$ V = 3.14 \times 16 \times 8 $$
$$ 16 \times 8 = 128 $$
$$ 128 \times 3.14 = 401.92 $$

So, the volume of the cylinder is $401.92\text{ cubic feet}$.

Step 3: Add the volumes together.
$$ \text{Total Volume} = \text{Volume of Prism} + \text{Volume of Cylinder} $$
$$ \text{Total Volume} = 1344 + 401.92 $$
$$ \text{Total Volume} = 1745.92 $$

Final Answer:
1745.92 cu ft