Question

A metal cylinder is melted and the whole mass is cast in the shape of a cube. What happens to the density? Give reasons.

Answer 1

Volume density is the mass per unit volume. So, if the mass of the body and the volume of the body is not changing then the density will be the same. Check if the mass or the volume of the body is changing to solve this question.

Formula used:
$\rho = \dfrac{m}{V}$
Where,
$\rho$ is the density
$m$ is mass
$V$ is volume

Complete step by step answer:
We know that,
$Density = \dfrac{{mass}}{{volume}}$
Let us explain this question by an example.
Let us take some water in a glass, say the glass is cylindrical in shape.
Now, Empty the glass in a vertical box so water will take the shape of the center.
In both these cases, even though the shape taken by the water is around, nothing has been added or taken out from under.
Therefore, Mass of the water and the volume of the water does not change and hence, the denting of water will be the same.
Using the same concept, we can say that,
Even though a metal cylinder is cast in the shape of a cube, its shape will change but its volume will remain the same.
Also, changing the shape of the metal will not change the propene of the metal. And same, nothing is being added or subtracted from the water; its mass will change either.
Therefore, there will be no change in the density of the metal.

So, the correct answer is “Option A”.

Note:
If it becomes difficult to understand some concept in a general sense. Then think about an example. Use the concept in that example and then try to generalize it. Just like we did in this question. So this question, we understand that if we do not change the metal or do not add any more in it. Then changing its shape will not change the density of that metal. Or anybody in a general sense.