Question

calculations (make sure you add the formulas, substitutions, and labels.)

1. mass: 60g, volume: 3cm³, density: ?
2. mass: 72g, volume: 8cm³, density: ?
3. density: 7g/cm³, volume: 9cm³, mass: ?
4. density: 11g/cm³, volume: 6cm³, mass: ?
5. density: 3g/cm³, mass: 21g, volume: ?
6. density: 20g/cm³, mass: 400g, volume: ?

Explanation:

To solve these density - mass - volume problems, we use the formula for density: $
ho=\frac{m}{V}$, where $
ho$ is density, $m$ is mass, and $V$ is volume. From this formula, we can also derive $m =
ho\times V$ and $V=\frac{m}{
ho}$. We will solve each of the six problems one by one.

Problem 1: Mass = 60g, Volume = 3$cm^{3}$, Find Density

Step 1: Recall the density formula

The formula for density is $
ho=\frac{m}{V}$, where $m$ is the mass and $V$ is the volume.

Step 2: Substitute the given values

We know that $m = 60g$ and $V=3cm^{3}$. Substituting these values into the formula, we get $
ho=\frac{60g}{3cm^{3}}$.

Step 3: Calculate the density

$\frac{60}{3}=20$, so $
ho = 20g/cm^{3}$.

Problem 2: Mass = 72g, Volume = 8$cm^{3}$, Find Density

Step 1: Recall the density formula

The formula for density is $
ho=\frac{m}{V}$.

Step 2: Substitute the given values

Here, $m = 72g$ and $V = 8cm^{3}$. Substituting into the formula, we have $
ho=\frac{72g}{8cm^{3}}$.

Step 3: Calculate the density

$\frac{72}{8}=9$, so $
ho=9g/cm^{3}$.

Problem 3: Density = 7$g/cm^{3}$, Volume = 9$cm^{3}$, Find Mass

Step 1: Recall the mass formula from density

The formula for mass is $m=
ho\times V$, where $
ho$ is density and $V$ is volume.

Step 2: Substitute the given values

We know that $
ho = 7g/cm^{3}$ and $V = 9cm^{3}$. Substituting these values, we get $m=7g/cm^{3}\times9cm^{3}$.

Step 3: Calculate the mass

$7\times9 = 63$, so $m = 63g$.

Problem 4: Density = 11$g/cm^{3}$, Volume = 6$cm^{3}$, Find Mass

Step 1: Recall the mass formula from density

The formula for mass is $m=
ho\times V$.

Step 2: Substitute the given values

Given $
ho=11g/cm^{3}$ and $V = 6cm^{3}$, we substitute to get $m = 11g/cm^{3}\times6cm^{3}$.

Step 3: Calculate the mass

$11\times6=66$, so $m = 66g$.

Problem 5: Density = 3$g/cm^{3}$, Mass = 21g, Find Volume

Step 1: Recall the volume formula from density

The formula for volume is $V=\frac{m}{
ho}$, where $m$ is mass and $
ho$ is density.

Step 2: Substitute the given values

We have $m = 21g$ and $
ho=3g/cm^{3}$. Substituting into the formula, we get $V=\frac{21g}{3g/cm^{3}}$.

Step 3: Calculate the volume

$\frac{21}{3}=7$, so $V = 7cm^{3}$.

Problem 6: Density = 20$g/cm^{3}$, Mass = 400g, Find Volume

Step 1: Recall the volume formula from density

The formula for volume is $V=\frac{m}{
ho}$.

Step 2: Substitute the given values

Given $m = 400g$ and $
ho=20g/cm^{3}$, we substitute to get $V=\frac{400g}{20g/cm^{3}}$.

Step 3: Calculate the volume

$\frac{400}{20}=20$, so $V = 20cm^{3}$.

Final Answers:

1. Density: $\boldsymbol{20g/cm^{3}}$
2. Density: $\boldsymbol{9g/cm^{3}}$
3. Mass: $\boldsymbol{63g}$
4. Mass: $\boldsymbol{66g}$
5. Volume: $\boldsymbol{7cm^{3}}$
6. Volume: $\boldsymbol{20cm^{3}}$

Answer:

To solve these density - mass - volume problems, we use the formula for density: $
ho=\frac{m}{V}$, where $
ho$ is density, $m$ is mass, and $V$ is volume. From this formula, we can also derive $m =
ho\times V$ and $V=\frac{m}{
ho}$. We will solve each of the six problems one by one.

Problem 1: Mass = 60g, Volume = 3$cm^{3}$, Find Density

Step 1: Recall the density formula

The formula for density is $
ho=\frac{m}{V}$, where $m$ is the mass and $V$ is the volume.

Step 2: Substitute the given values

We know that $m = 60g$ and $V=3cm^{3}$. Substituting these values into the formula, we get $
ho=\frac{60g}{3cm^{3}}$.

Step 3: Calculate the density

$\frac{60}{3}=20$, so $
ho = 20g/cm^{3}$.

Problem 2: Mass = 72g, Volume = 8$cm^{3}$, Find Density

Step 1: Recall the density formula

The formula for density is $
ho=\frac{m}{V}$.

Step 2: Substitute the given values

Here, $m = 72g$ and $V = 8cm^{3}$. Substituting into the formula, we have $
ho=\frac{72g}{8cm^{3}}$.

Step 3: Calculate the density

$\frac{72}{8}=9$, so $
ho=9g/cm^{3}$.

Problem 3: Density = 7$g/cm^{3}$, Volume = 9$cm^{3}$, Find Mass

Step 1: Recall the mass formula from density

The formula for mass is $m=
ho\times V$, where $
ho$ is density and $V$ is volume.

Step 2: Substitute the given values

We know that $
ho = 7g/cm^{3}$ and $V = 9cm^{3}$. Substituting these values, we get $m=7g/cm^{3}\times9cm^{3}$.

Step 3: Calculate the mass

$7\times9 = 63$, so $m = 63g$.

Problem 4: Density = 11$g/cm^{3}$, Volume = 6$cm^{3}$, Find Mass

Step 1: Recall the mass formula from density

The formula for mass is $m=
ho\times V$.

Step 2: Substitute the given values

Given $
ho=11g/cm^{3}$ and $V = 6cm^{3}$, we substitute to get $m = 11g/cm^{3}\times6cm^{3}$.

Step 3: Calculate the mass

$11\times6=66$, so $m = 66g$.

Problem 5: Density = 3$g/cm^{3}$, Mass = 21g, Find Volume

Step 1: Recall the volume formula from density

The formula for volume is $V=\frac{m}{
ho}$, where $m$ is mass and $
ho$ is density.

Step 2: Substitute the given values

We have $m = 21g$ and $
ho=3g/cm^{3}$. Substituting into the formula, we get $V=\frac{21g}{3g/cm^{3}}$.

Step 3: Calculate the volume

$\frac{21}{3}=7$, so $V = 7cm^{3}$.

Problem 6: Density = 20$g/cm^{3}$, Mass = 400g, Find Volume

Step 1: Recall the volume formula from density

The formula for volume is $V=\frac{m}{
ho}$.

Step 2: Substitute the given values

Given $m = 400g$ and $
ho=20g/cm^{3}$, we substitute to get $V=\frac{400g}{20g/cm^{3}}$.

Step 3: Calculate the volume

$\frac{400}{20}=20$, so $V = 20cm^{3}$.

Final Answers:

1. Density: $\boldsymbol{20g/cm^{3}}$
2. Density: $\boldsymbol{9g/cm^{3}}$
3. Mass: $\boldsymbol{63g}$
4. Mass: $\boldsymbol{66g}$
5. Volume: $\boldsymbol{7cm^{3}}$
6. Volume: $\boldsymbol{20cm^{3}}$