Question

practice: density calculations
answer the following questions. make sure to show all work to receive credit. you may need a separate sheet of paper.

1. find the volume of a box measuring 2 cm by 7 cm by 3 cm.
2. an object placed in a graduated cylinder raises the volume from 12.2 ml to 14.5 ml. find the volume of the object.
3. find the volume of a cube measuring 5 cm on each side.
4. find the density of the box in #1 if it has a mass of 20 g.
5. find the density of the object in #2 if it has a mass of 4 g.
6. find the density of the cube in #3 if it has a mass of 100 g.
7. find the mass of an object that has a density of 1.5 g/cm³ and has a volume of 8 cm³.
8. find the volume of an object with a density of 3.1 g/ml and a mass of 12 g.
9. find the mass of a cube that has a density of 2.7 g/ml and measures 3 cm on each side.
10. challenge: find the density of a soda can with a radius of 3.25 cm, a height of 12.2 cm, and a mass of 40 g.

Explanation:

Step1: Calculate volume of box in #1

Use formula $V = l\times w\times h$, where $l = 2$ cm, $w = 7$ cm, $h = 3$ cm. So $V=2\times7\times3 = 42$ $cm^{3}$.

Step2: Calculate volume of object in #2

Volume of object is the change in volume of graduated - cylinder. $V=14.5 - 12.2=2.3$ mL.

Step3: Calculate volume of cube in #3

Use formula $V = s^{3}$, where $s = 5$ cm. So $V = 5^{3}=125$ $cm^{3}$.

Step4: Calculate density of box in #4

Density formula is $
ho=\frac{m}{V}$. Given $m = 20$ g and $V = 42$ $cm^{3}$ from Step1. So $
ho=\frac{20}{42}\approx0.48$ g/$cm^{3}$.

Step5: Calculate density of object in #5

Given $m = 4$ g and $V = 2.3$ mL from Step2. So $
ho=\frac{4}{2.3}\approx1.74$ g/mL.

Step6: Calculate density of cube in #6

Given $m = 100$ g and $V = 125$ $cm^{3}$ from Step3. So $
ho=\frac{100}{125}=0.8$ g/$cm^{3}$.

Step7: Calculate mass of object in #7

Use formula $m=
ho\times V$. Given $
ho = 1.5$ g/$cm^{3}$ and $V = 8$ $cm^{3}$. So $m = 1.5\times8=12$ g.

Step8: Calculate volume of object in #8

Use formula $V=\frac{m}{
ho}$. Given $m = 12$ g and $
ho = 3.1$ g/mL. So $V=\frac{12}{3.1}\approx3.87$ mL.

Step9: Calculate mass of cube in #9

First, find volume of cube. $V = s^{3}$, where $s = 3$ cm, so $V = 3^{3}=27$ $cm^{3}=27$ mL. Then use $m=
ho\times V$. Given $
ho = 2.7$ g/mL, so $m = 2.7\times27 = 72.9$ g.

Step10: Calculate density of soda - can in #10

Volume of cylinder formula is $V=\pi r^{2}h$. Given $r = 3.25$ cm and $h = 12.2$ cm. So $V=\pi\times(3.25)^{2}\times12.2\approx\pi\times10.5625\times12.2\approx403.7$ $cm^{3}$. Given $m = 40$ g. Then $
ho=\frac{m}{V}=\frac{40}{403.7}\approx0.10$ g/$cm^{3}$.

Answer:

1. $42$ $cm^{3}$
2. $2.3$ mL
3. $125$ $cm^{3}$
4. $\approx0.48$ g/$cm^{3}$
5. $\approx1.74$ g/mL
6. $0.8$ g/$cm^{3}$
7. $12$ g
8. $\approx3.87$ mL
9. $72.9$ g
10. $\approx0.10$ g/$cm^{3}$