Question

An ancient gold coin is 2.2 cm in diameter and 3.0 mm thick.If the density Of gold is 19.3g/cm^3, what is the mass of the coin? If gold costs $125.00 per gram ,how much is the gold worth?

Answer 1

Thickness=height since it is a coin
A coin with thickness as its height makes it a cylinder

Volume of a cylinder=pi x height x (radius)^2
Diameter= 2 x radius
2.2cm/2=1.1cm
r=1.1cm

Convert 3.0mm to cm to make all units the same and because the density is in cm
1mm=0.10cm
then 3mm is equal to 0.30cm

Volume=3.14 x 0.30cm x (1.1cm)^2=1.139 cm^3

Density=mass/volume
19.3g/cm^3=mass/1.139cm^3
Mass=19.3g/cm^3 x 1.139cm^3
Mass=21.982g

Price=number of grams x $125.00
Price=21.982 x $1.25
Price=$2747.83 or $2.7 x10^3