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?

1 Answer
Jan 3, 2018

The platinum rectangle weighs more.


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) = 2.00cm*1.00cm*4.00cm = 8.00cm^3#
#V_(p) = 1.4cm*2.9cm*2.0cm = 8.1cm^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:
#8.00cm^3# x #19.3g/(cm^3)# = 154 g of gold
#8.1cm^3# x #21.4g/(cm^3)# = 170 g of platinum