# The density of gold is 19.3 g/cm3 and that of platinum is 21.4 g/cm3. What of the following weighs more: A rectangle of gold measuring 2.00 cm x 1.00 cm x 4.00 cm or a rectangle of platinum measuring 0.045 ft x 0.095 ft x 0.065 ft?

Jan 3, 2018

The platinum rectangle weighs more.

#### Explanation:

To solve this problem, we first need to find the volume of the rectangles and then multiply by their densities to find the mass of each rectangle.

Finding voulme of a rectangle:
All you need to do is multiply the length, width and height, which are all given.
${V}_{g} = 2.00 c m \cdot 1.00 c m \cdot 4.00 c m = 8.00 c {m}^{3}$
${V}_{p} = 1.4 c m \cdot 2.9 c m \cdot 2.0 c m = 8.1 c {m}^{3}$

Don't forget to convert the units of the platinum rectangle from ft to cm (like I did; it is a common mistake but don't overlook the units)!

Multiply by density:
$8.00 c {m}^{3}$ x $19.3 \frac{g}{c {m}^{3}}$ = 154 g of gold
$8.1 c {m}^{3}$ x $21.4 \frac{g}{c {m}^{3}}$ = 170 g of platinum