What is thev volume of a 1 carat diamond if 1 carat is 200mg?

Question

1.what is the price of a 1 carat diamond if 1 microgram is 0.75 pesos?

help me plz..thanks

Answer 1

For the volume, there isn't enough info. You need the density of diamond as well. The density of diamond is about 3.5 g/1cm³.

So the volume of the diamond can be calculated:

Volume = Mass / Density

Volume = 0.2g / (3.5g/1cm³)

Volume = 0.2g * 1cm³/3.5g

Volume = 0.2gcm³ / 3.5g

Volume = 0.2/3.5 cm³ = 2/35 cm³

The volume of the diamond ≈ 2/35 cm³

For the second one, I'm assuming that Pesos is the currency used in Mexico (which it is) and that diamonds cost 0.75 Pesos per microgram in Mexico. (Which is what your question said)

So the cost of a 1 carat diamond in Pesos:

200 mg = 200 000 micrograms.

200 000micrograms * 0.75 Pesos/microgram = 150 000 Pesos

So a 1 carat diamond would cost 150 000 Mexican Pesos.

Which at the current exchange rate is about US$14 503.65

or £7 306.62

Answer 2

To find the volume, you will also need to know the density.  Density is Mass per unit Volume.  You have the mass (200 mg).  Once you know the density, just divide the mass by the density.

To find the cost of the diamond you would multiply the cost per milligrams (0.75 pesos/ug) by the mass (200 mg x 1000 ug/mg).  So...

Cost  = 0.75 pesos/mg x 200  mg x 1000 ug/mg

There you have it.