Question

Calculate the density of a solid substance if a cube measuring 2.72 cm on one side has a mass of 130g.

Answer 1

density \(\varrho\), is equal to the mass \(m\), per volume \(V\)

\[\varrho = m/V\]



Calculate the volume of the cube

Answer 2

How do you calculate the volume of the cube?

Answer 3

the volume \(V\), of a cube is equal to the length of its sides \(s\), cubed.
\[V =s^3\]

Answer 4

so you would cube the 2.72?

Answer 5

you are given that the sides are \(s=2.72[\text{cm}]\)

Answer 6

What volume does this make?

Answer 7

If you cube the 2.72 cm?

Answer 8

yes,

Answer 9

20.123648 cm^3

Answer 10

good, thats the volume,

now the density is
\[\varrho = m/V = \frac{130[\text g]}{20.123648 [\text{cm}^3]}=\]

Answer 11

6.460061317g/cm^3

Answer 12

yeah thats it,
now you might want to round to 3 significant figures, (because the values given are themselves only accurate to 3sig.figs)

Answer 13

So 6.460

Answer 14

(that is four significant figures)

Answer 15

Whoops
6.46

Answer 16

yeah, i would leave my final answer as \(\varrho=6.46\,[\text g/\text{cm}^3]\)

Answer 17

Alright thank you. There is another question like it wanting to calculate the mass of a cube of the same substance measuring 7.51cm on one side.

Answer 18

OK, well since the substance is the same, the density (an intrinsic quality) will remain the same

Answer 19

rearranging\[\varrho=m/V\]
we get\[m =\varrho\cdot V\]

again the volume of a cube is \(s^3\)

Answer 20

7.51^3 = 423.564751

Answer 21

now multiply that, by the density we found earlier

Answer 22

2736.228291

Answer 23

and what are the units?

Answer 24

grams

Answer 25

since mass was being calculated for

Answer 26

yeah, so what is our final answer with units (and to 3sig.figs)

Answer 27

Alright and if it wants it in scientific notation would it be 2.73 x 10^3?

Answer 28

\[2.74 \times 10^3\,[\text g]=2.74\,[\text{kg}]\]

Answer 29

Thanks. Didn't notice the 6 there.

Answer 30

Thanks for the help!

Answer 31

notice that the ratio of volumes \(424\,[\text{cm}^3]/20.1\,[\text{cm}^3]\approx21\), is equal to the ratio of masses \(2740\,[\text g]/130\,[\text g]\approx21\)

Answer 32

(as we should expect for a substance of constant density )

Answer 33

I didn't notice that. That's interesting and that does make sense for it to.