Understand the terms. The shape of the Superdome is what's known as an imperfect ellipsoidal dome. An ellipsoid is basically a 3 dimensional oval, kind of like an egg. A hemi-ellipsoid is half of an ellipsoid. The Superdome can be approximated as an imperfect hemi-ellipsoid. It is imperfect because the walls do not curve inwards until they reach the dome roof. A diameter of an ellipsoid is the length from one side to the other through a straight line at the longest, widest, and tallest point. A radius is half of a diameter, or the distance from the center of the ellipsoid.
Gather the appropriate measurements. You can work out the total volume for a hemi-ellipsoid with the length, the width, and the height. The Superdome is about 689 feet long, 400 feet wide, and 253 feet tall.
Convert the measurements to fit the formula. The formula is (4/3¶ AB(C2)) / 2. A, B, and C are the three radii of the ellipsoid. To calculate the length radius (A) divide the total length by 2. This is also true for the width radius (B). However, since the Superdome is a hemi-ellipsoid you must multiply the height radius by two, which is the same as the height diameter. Apply the Superdome's measurements to this process to get A=344.5, B=200, and C=253.
Multiply pi (¶) by 4/3. Pi represents the ratio of a circle's circumference to its diameter. Its value is always about 3.14. Because the Superdome is more like an ellipsoid than a circle, it is necessary to compensate. When you multiply pi times 4/3 you get about 4.19.
Apply the formula. You'll get (4.19x344.5x200x253) / 2. You divide by two because it is half of an ellipsoid. This comes out to 36,519,411.5. So the volume of a hemi-ellipsoid with the Superdome's measurement is about 37 million cubic feet. Because the Superdome is imperfect and all measurements were approximated, this is an approximation as well, but you can see the process.