On the different densities of Philippine coins

Different Philippine coins

Source: https://bryologue.files.wordpress.com/2012/09/a-handful-of-philippine-coins.jpg

This lab activity's purpose was to determine the densities of different Philippine coins namely: 5 cents, 10 cents, 25 cents, 1 peso, 5 peso, and 10 peso. The density (generally) is given by: 

                                                                                 ρ=mV

The trick in the 5 centavo coin is that it has a hole in between. To determine its density we just need to subtract the diameter of the hole from the diameter of the coin. Then we use the equation given that 

V=πr2h

Below are our data:

5¢ D = 15.46 ± 0.02 mm 

d = 3.68 ± 0.02 mm 

h = 1.44 ± 0.02 mm 

m = 1.9 ± 0.05 mm

ρ5cρ5cρ5c==≈4mπh(D2−d2)4(1.9 g)π(1.44 mm)((15.46 mm)2−(3.68 mm)2)=7.45×10−3 g/mm37.45 mg/mm3

10¢ d = 11.88 ± 0.02 mm 

h = 1.54 ± 0.02 mm 

m = 2.5 ± 0.05 g

ρ10cρ10cρ10c==≈4mπd2h4(2.5 g)π(16.88 mm)2(1.54 mm)=7.25×10−3g/mm37.25 mg/mm3

And solving in the same way how we solved the density of 10 cents, the densities of other coins are:

25¢ d = 19.92 ± 0.02 mm 

h = 1.72 ± 0.02 mm 

m = 3.6 ± 0.05 g

density = 

6.72±0.172 mg/mm3

PHP 1 d = 23.84 ± 0.02 mm 

h = 1.86 ± 0.02 mm 

m = 5.3 ± 0.05 g

density =

6.38±0.129 mg/mm3

PHP 5 d = 26.78 ± 0.02 mm 

h = 1.88 ± 0.02 mm 

m = 7.7 ± 0.05 g 

density = 

7.27±0.125 mg/mm3