Question

1. a thin glass bottle holds 25 ml of liquid and has a mass of 19 grams. calculate the density.
2. a bar of soap is 12 cm tall, 6 cm wide, and 10 cm long. it has a mass of 415 grams. what is the density of the bar of soap.
3. a sheet of metal is 2 cm wide, 10 cm tall, and 15 cm long. it was 4 grams. what is the density?
4. a pencil has a density of.875 g/ml. it has a mass of 3.5 grams. what is the volume?

Explanation:

Step1: Recall density formula

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

Step2: Solve problem 4

Given $m = 19$ g and $V=25$ ml. Substitute into the formula: $
ho=\frac{19}{25}= 0.76$ g/ml.

Step3: Solve problem 5

First, find the volume of the soap bar. The volume of a rectangular - prism $V = l\times w\times h$, where $l = 10$ cm, $w = 6$ cm and $h = 12$ cm. So $V=10\times6\times12 = 720$ $cm^{3}$. Then, using $
ho=\frac{m}{V}$ with $m = 415$ g, we get $
ho=\frac{415}{720}\approx0.58$ g/$cm^{3}$.

Step4: Solve problem 6

Find the volume of the metal sheet. $V=l\times w\times h$, with $l = 15$ cm, $w = 2$ cm and $h = 10$ cm. So $V=15\times2\times10=300$ $cm^{3}$. Using $
ho=\frac{m}{V}$ with $m = 4$ g, we have $
ho=\frac{4}{300}\approx0.013$ g/$cm^{3}$.

Step5: Solve problem 7

Given $
ho = 0.875$ g/ml and $m = 3.5$ g. From $
ho=\frac{m}{V}$, we can solve for $V$. Rearranging the formula gives $V=\frac{m}{
ho}$. Substituting the values, we get $V=\frac{3.5}{0.875}=4$ ml.

Answer:

Problem 4: 0.76 g/ml
Problem 5: Approximately 0.58 g/$cm^{3}$
Problem 6: Approximately 0.013 g/$cm^{3}$
Problem 7: 4 ml