Not exactly a Geography question, but here goes. Since the units change when you’re measuring area or volume, let’s get those numbers first.
A linear mile = 5,280 linear feet (ft)
A square mile = 27,878,400 square feet (ft²)
A cubic mile = 147,197,952,000 cubic feet (ft³)
Ok, big numbers, right? So let’s just do the problem in feet to start with, and convert back later.
12 mi x 5280 ft/mi = 63360 ft (east west distance)
10 mi x 5280 ft/mi = 52800 ft (north south distance)
Now for the area we simply multiply e/w by n/s
63360 ft x 52800 ft = 3345408000 ft²
To get that back into miles (SQUARE miles, remember) divide by 27878400.
3345408000 ft² / 27878400 ft²/mi² = 120 mi² (Surface Area)
Actually, since this is in whole miles, we could have simply multiplied 10 x 12 and gotten the same answer.
But for the volume, since the depth is only a fraction of a whole mile, we’ll need those numbers in feet.
Going back to our surface area of 3345408000 ft², we multiply that by the “average” depth (only in school!) of twelve feet.
3345408000 ft² x 12 ft = 40144896000 ft³
To get that into cubic miles, we divide by 147197952000.
40144896000 ft³ / 147197952000 ft³/mi³ = 0.27272727272727272727 mi³
In fraction form, that’s 3/11’s of a cubic mile
So your answers are:
3345408000 ft² or 120 mi²
40144896000 ft³ or 0.2727272727272727 mi³ or 3/11 mi³