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

1. UnkleRhaukus

density $$\varrho$$, is equal to the mass $$m$$, per volume $$V$$ $\varrho = m/V$ Calculate the volume of the cube

2. anonymous

How do you calculate the volume of the cube?

3. UnkleRhaukus

the volume $$V$$, of a cube is equal to the length of its sides $$s$$, cubed. $V =s^3$

4. anonymous

so you would cube the 2.72?

5. UnkleRhaukus

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

6. UnkleRhaukus

What volume does this make?

7. anonymous

If you cube the 2.72 cm?

8. UnkleRhaukus

yes,

9. anonymous

20.123648 cm^3

10. UnkleRhaukus

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

11. anonymous

6.460061317g/cm^3

12. UnkleRhaukus

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

13. anonymous

So 6.460

14. UnkleRhaukus

(that is four significant figures)

15. anonymous

Whoops 6.46

16. UnkleRhaukus

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

17. anonymous

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.

18. UnkleRhaukus

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

19. UnkleRhaukus

rearranging$\varrho=m/V$ we get$m =\varrho\cdot V$ again the volume of a cube is $$s^3$$

20. anonymous

7.51^3 = 423.564751

21. UnkleRhaukus

now multiply that, by the density we found earlier

22. anonymous

2736.228291

23. UnkleRhaukus

and what are the units?

24. anonymous

grams

25. anonymous

since mass was being calculated for

26. UnkleRhaukus

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

27. anonymous

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

28. UnkleRhaukus

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

29. anonymous

Thanks. Didn't notice the 6 there.

30. anonymous

Thanks for the help!

31. UnkleRhaukus

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

32. UnkleRhaukus

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

33. anonymous

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