Question

A cuboid has diagonal x,y,z find its volume

Answer 1

A cuboid has 2 diagonal, both equal of length = root over sum of squares of sides. It is not possible to get volume of the cuboid from that.

But since X, Y and Z are distinct, I assume they are diagonals of 3 faces.

Let the sides be l, b and h. Then

l2+b2=X2

l2+h2=Y2

h2+b2=Z2

Then

2l2=X2+Y2−Z2

2b2=X2−Y2+Z2

2h2=−X2+Y2+Z2

From this you will get the required answer with volume = l*b*h