Question

are the volumes of water and ice formed with same amount of water equal ? prove it

Answer 1

No, they aren’t equal.
The density of water is 1.00 g/cm³.
So the volume of 100 g of water is100 g×1 cm31 g=100 cm3
The density of ice is 0.92 g/cm³.
So the volume of 100 g of ice is100 g×1 cm30.92 g=109 cm3
The volume of ice is greater than that of the same volume of water.That's why ice floats on water.

Answer 2

No, the volumes of same amount of water and ice are not equal. It is because their densities are different.

Proof:
Let the amount of water taken = M gram
We know that density = mass×volume
⇒ volume = mass/density

If it is water,
mass = M g
density = 1 g/cm³
volume of water = mass/density = M/1 = M cm³

If it is ice,
mass = M g
density = 0.916 g/cm³
volume of ice= mass/density = M/0.916 = 1.09M cm³

As we can see, the volume of ice is 1.09M cm³ whereas the volume of water is M cm³. So the volumes are not equal.