To determine which formulas correctly represent the mass or volume in terms of density, let's start with the given formula for density and solve for mass and volume.
The original formula is:
[tex]\[ D = \frac{M}{V} \][/tex]
### 1. Solving for Mass (M):
To find the mass [tex]\( M \)[/tex] in terms of density [tex]\( D \)[/tex] and volume [tex]\( V \)[/tex], we need to rearrange the original formula:
[tex]\[ D = \frac{M}{V} \][/tex]
Multiply both sides by [tex]\( V \)[/tex] to isolate [tex]\( M \)[/tex]:
[tex]\[ D \times V = \frac{M}{V} \times V \][/tex]
[tex]\[ D \times V = M \][/tex]
So, the formula for mass is:
[tex]\[ M = D \times V \][/tex]
### 2. Solving for Volume (V):
To find the volume [tex]\( V \)[/tex] in terms of mass [tex]\( M \)[/tex] and density [tex]\( D \)[/tex], we start again with the original formula:
[tex]\[ D = \frac{M}{V} \][/tex]
Multiply both sides by [tex]\( V \)[/tex] to clear the denominator:
[tex]\[ D \times V = M \][/tex]
Now, divide both sides by [tex]\( D \)[/tex] to solve for [tex]\( V \)[/tex]:
[tex]\[ V = \frac{M}{D} \][/tex]
So, the formula for volume is:
[tex]\[ V = \frac{M}{D} \][/tex]
### 3. Verification of Given Formulas:
Let's verify each of the provided formulas:
1. [tex]\[ M = \frac{D}{V} \][/tex]
- This is incorrect. The correct formula for mass is [tex]\( M = D \times V \)[/tex].
2. [tex]\[ V = \frac{D}{M} \][/tex]
- This is incorrect. The correct formula for volume is [tex]\( V = \frac{M}{D} \)[/tex].
3. [tex]\[ V = \frac{M}{D} \][/tex]
- This is correct, as we derived above.
4. [tex]\[ M = D \times V \][/tex]
- This is correct, as we derived above.
5. [tex]\[ V = D \times M \][/tex]
- This is incorrect. The correct formula for volume is [tex]\( V = \frac{M}{D} \)[/tex].
6. [tex]\[ M = \frac{V}{D} \][/tex]
- This is incorrect. The correct formula for mass is [tex]\( M = D \times V \)[/tex].
Therefore, the two correct formulas are:
[tex]\[ M = D \times V \][/tex]
[tex]\[ V = \frac{M}{D} \][/tex]
So, the correct answers are:
- [tex]\[ V = \frac{M}{D} \][/tex]
- [tex]\[ M = D \times V \][/tex]
