Question

At one point in time, the price of gold was about $1400 per ounce, while that of silver was about $20 an ounce. The "ounce" in this case is the troy ounce, which is equal to 31.1035 g. (The more familiar avoirdupois ounce is equal to 28.35 g.) The density of gold is 19.3 g/cm3 and that of silver is 10.5 g/cm3.

A. If you found a spherical gold nugget worth $5 million, what would be its diameter?

ANSWER: ______________ cm

B. How much would a silver nugget of that size be worth?

ANSWER: $ ____________

Answer 1

Gold nugget diameter 22,24 cm

Silver nugget price 38860 $

Explanation:

Gold price 1400 $ /ou 1 ounce = 31.1035 grs

so 1400 /31.1035

Gold price is 45,01 $/grs.

If a nugget worth 5000000 $ then 5000000/ 45.01

a nugget mass : 111086,43 grs

Now gold density is d = 19.3 grs/cm³

And she volume is V = 4/*π*r³

d = m/V V = m/d V = 111086.43/19.3 cm³

V = 5755,77 cm³

Now V of the sphere is V = 5755,77 = 4/3*π*r³

r³ =3*5755,77 / 4π r³ = 1374,79

r = 11.12 cm 2r = 22,24 = Φ (sphere diameter)

B) d (silver) = m/V m = d*V

V = 5755,77 cm³ The same size the same volume

m = 10,5 * 5755,77 [grs/cm³ * cm³] m = 60435,59 grs

Silver nugget worth :

20 $ /ou 20/31.1035 = 0.643 $ /grs

Price 0,643 * 60435,59 = 38860 $