1. ## conversions

As you might know, there are now businesses asking you to send in your old jewelry in exchange for cash. Imagine you have a solid gold sphere of 15.7 mm diameter which you decide to send in for cash. If the company offers $125 per ounce of gold, how much money will they send you given that the density of gold is 19.31 g/cm^3. 1 ounce = 28.3495231 grams 1 cm^3 = 1000mm^3 19.31g/cm^3 x 1 ounce/28.3495231 g x cm^3/1000mm^3 = = 4.8275 ounces/mm^3 (15.7mm)^3 = 3,869.893mm^3 x 4.8275 ounces/mm^3 = 18,681.90846 ounces x$ 125 = 2,335, 238.557 dollars...which leads me to believe this is wrong.

2. $\displaystyle V = \frac{4}{3}\pi \left(\frac{1.57}{2}\right)^3 = 2.026... cm^3$

$\displaystyle M = \rho V = 19.31 \cdot 2.026... = 39.1273... g$

$\displaystyle \frac{39.1273...}{28.3495...} \cdot 125 = 172.52$ dollars

must be a very old problem ... gold is going for much more than \$125 per ounce these days.

3. I don't get the 1.57/2 part.

4. Originally Posted by A Beautiful Mind
I don't get the 1.57/2 part.
15.7 mm = 1.57 cm = the diameter.

So the radius = 1.57/2 cm.