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
kai
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) = 2.00cm*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

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