For those who do not prefer converting to AE cubits, here is the calculation in inches:

Petrie's measures:

Inside length: 78.06 inches
Inside width: 26.81 inches
Inside height: 34.42 inches

78.06 x 26.81 = 2092.7886 (area of inside base of coffer in square inches)

2092.7886 divided by pi = 666.1553

The square root of 666.1553 is 25.8099 inches (radius of a circle with an area of 2092.7886 square inches)

25.8099 cubed is 17193.4580

17193.4580 times 4/3 times pi = 72019.7885 cubic inches (volume of a sphere with a radius of 25.8099 inches)

72019.7885 divided by 78.06 (inside length) = 922.6209

922.6209 divided by 26.81 (inside width) = 34.413 inches (inside height)

34.413 inches is within 1/100th of an inch of the measured inside height of the coffer.