How many rundlets are there in 218 in3?
Some conversion factors that may be useful are given below:
1.00 barrel = 42.0 gal
1.00 gal = 231 in3
1.00 gal = 3.78 L
1.00 rundlet = 6.81 × 104 mL
1.00 L = 1000.0 mL
1.00 barrel = 4.00 firkins

218 "cubic inch" = 0.05238 "rundlets"

Explanation:

From the conversion factors;

1.00 gal = 231 in3 = 3.78 L

But;

1.00 rundlet = 6.81 × 104 mL = 68.1 L (Converting to L by dividing by 1000)

231 in3 = 3.78 L

218 in3 = x

x = (218 * 3.78 ) / 231

x = 3.5673L

But 1 rudlet = 68.1 L

x rundlet = 3.5673L

x = (3.5673 * 1 ) / 68.1

x = 0.05238

the density of gold = 19.3 g/cm3

the relation between density and mass and volume is

density = mass / volume

given :

mass of gold = 13 g

density = 13g / volume = 19.3

volume = 13 /19.3 = 0.67 cm^3

thus volume of gold nugget = 0.67 cm^3