This is how I do it when designing enclosures as it is the fastest way to get the dimensions you want:

Take the total volume cubic feet and convert it to cubic inches:

1 ft^3 = 1728 in^3

So...

0.42 ft^3 * 1728 = 725.76 in^3

This means the internal volume of the enclosure needs to be 725.76 in^3

Then I add the probable volume the back side of the driver will occupy. You don't provide any data on the driver, not even diameter, so I have no idea what to add to the volume. Just for fun, I'll add 200 in^3 for a total box volume of 925.76 in^3.

Next, I figure out if there are any limitations on the dimensions I cannot exceed - like perhaps the distance between studs which is usually 16 inches. To allow for a little imperfection in the studs, I'll say the width of the enclosure cannot exceed 15 inches. So, the first dimension is fixes at 15 inches. If you are using 0.75 inch thick MDF or Plywood, then the internal width distance cannot exceed 13.5 inches (1.5 inches used by the two side walls of the box).

So, you can divide the total internal volume by the first fixed dimension to get the squared distance for the rest of the enclosure dimensions:

925.76 in^3 / 13.5 in = 68.575 in^2

If the next fixed dimension is, say 4 inches deep internally (5.5 inches deep externally), then the next equation is:

68.575 in^2 / 4 in = 17.144 in.

Thus, the internal dimensions of the enclosure to reach 0.42 ft^3 are:

13.5" x 4" x 17.15"

External dimensions (assuming 0.75" thick panels) are:

15" x 5.5" x 18.65"

I hope that helps.