Block A of an unknown metal has a volume of
125 cm3. Block B of a different metal has a volume
of 145 cm3. If block A has a greater mass than block
B, what can be said of the relative densities of the
two metals? (Assume that both blocks are solid.)
Block A has a greater mass in 125 cm^3
than Block B has in 145 cm^3
so Block A is more dense.
To determine the relative densities of the two metals, we need to compare their masses and volumes.
Given that the volume of block A is 125 cm^3 and the volume of block B is 145 cm^3, we can see that block B has a larger volume than block A.
Now, since block A has a greater mass than block B, we can conclude that the density of block A is greater than the density of block B.
In general, density is calculated by dividing the mass of an object by its volume.
Mathematically, density (D) can be expressed as:
D = Mass / Volume
Since block A has a greater mass than block B, and both blocks are solid, we can conclude that the density of the metal in block A is greater than the density of the metal in block B.
To determine the relative densities of the two metals, we need to compare their masses in relation to their volumes. Density is defined as mass divided by volume (ρ = m/V).
Let's assume the density of metal A is ρA and the density of metal B is ρB.
Given that block A has a greater mass than block B, we can express this as mA > mB, where mA is the mass of block A and mB is the mass of block B.
We know the volume of block A (VA) is 125 cm³, and the volume of block B (VB) is 145 cm³.
From the definition of density, we have:
ρA = mA/VA (equation 1)
ρB = mB/VB (equation 2)
Since we are comparing the densities, we can divide equation 1 by equation 2:
ρA/ρB = (mA/VA) / (mB/VB)
ρA/ρB = (mA * VB) / (VA * mB)
Since mA > mB, we can conclude that (mA * VB) > (VA * mB). Thus, ρA/ρB > 1.
Therefore, we can say that the relative density of metal A is greater than the relative density of metal B.