Question

A kilderkin is an old unit of volume equal to half a barrel or two firkins. It was used as a standard size for brewery casks. A barrel was equal to 36 gallons, and a hogshead was 1.5 barrels. A hogshead was approximately 250 liters. Approximately how many liters were in a firkin?​

Answer 1

Hint: Now the given question is a basic conversion question. So first we have to find the general equation explaining the relationship between the given two units. After that we have to find the specific value for the value given in the question.

Complete step-by-step solution:
Given
$
\Rightarrow 1\;{\text{Kilderkin}} = \dfrac{1}{2}\;{\text{Barrel}} = 2\;{\text{Firkins}}.....................\left( i \right) \\
\Rightarrow 1\;{\text{Barrel}} = 36\;{\text{Gallons}}........................................\left( {ii} \right) \\
\Rightarrow 1\;{\text{Hogshead}}\; = 1.5\;{\text{Barrels}} = 250\;{\text{Liters}}................................\left( {iii} \right) \\
 $
Now from the given information we have to find the relationship between liters and firkin.
Now from (iii) we can find the relationship between barrel and liter.
Such that:
\[
\Rightarrow 1.5\;{\text{Barrels}} = 250\;{\text{Liters}} \\
\Rightarrow 1\;{\text{Barrel}} = \dfrac{{250}}{{1.5}}\;{\text{Liters}} \\
\Rightarrow 1\;{\text{Barrel}} = \dfrac{{2500}}{{15}}\;{\text{Liters}} \\
\Rightarrow 1\;{\text{Barrel}} = \dfrac{{500}}{3}\;{\text{Liters}}....................\left( {iv} \right) \\
 \]
Also from (i) we can get the relationship between barrel and firkins, such that:
\[
\Rightarrow \dfrac{1}{2}\;{\text{Barrel}} = 2\;{\text{Firkins}} \\
\Rightarrow 1\;{\text{Barrel}} = 4\;{\text{Firkins}}.......................\left( v \right) \\
 \]
Now on observing (iv) and (v) we can see that the RHS of the equation is same such that we can equate the LHS of the equation and find how many liters are in a firkin.
Such that from (iv) and (v) we can write:
$
\Rightarrow \dfrac{{500}}{3}{\text{Litres}} = 4\;{\text{Firkins}} \\
\Rightarrow 1\;{\text{Firkins}} = \dfrac{{500}}{{3 \times 4}}{\text{Litres}} \\
\Rightarrow 1\;{\text{Firkins}} = \dfrac{{500}}{{12}}{\text{Litres}} \\
\Rightarrow 1\;{\text{Firkins}} = 41.666\;{\text{Litres}} \\
 \Rightarrow \approx 42\;{\text{Litres}}........................\left( {vi} \right) \\
 $

Therefore there are approximately 42 liters in a firkin.

Note: While approaching similar conversion questions the above method is widely preferred. Also until the adoption of the imperial system the beer kilderkin was defined as 18 beer gallons. With the adoption of the imperial system the kilderkin was redefined to be 18 imperial gallons, which is exactly 81.82962 liters.