Answer:
Yes
Step-by-step explanation:
The density of the object does not change when it is broken in more pieces, therefore Maria will be able to find the density of the material.
In fact, by breaking the object, then she can take only one piece, and by measuring the mass of this piece and its volume she will be able to calculate the density of the material by using the formula:

where
m is the mass of the piece
V is its volume
d is the density
And the density will be the same for every piece, since they are made by the same material, and the density depends only on the properties of the material itself.