A manufacturer of insulated cups has three machines that, when all working, produce the metal shell for 1225 cups per day. When only machine A and machine B are operational, they produce
675 shells per day. When only machine B and machine C are operational, they produce 1000
shells per day. Determine the daily quantity of metal shells produced by each machine.
Solve using augmented matrices

The diagonal forms a right isosceles triangle whose hypotenuse is x√2 where x is the length of a side of the square face
so, x√2=5
x=5/√2
x=5/1.414
x=3.536 cm
you can also use the Pythagorean Theorem to get the length of a side, x
5^2=x^2+x^2
25=2x^2
x^2=25/2
x^2=12.5
x=√12.5
x=3.535 cm
the volume is V=3.536^3
V=3.536*3.536*3.536
V=44.2 cm^3
my answer has more accuracy, therefore you choose D) which is closest to my answer