Answer
(a) $67~mutchkins$
(b) $1~noggin=0.031~gal$
Work Step by Step
See conversion factors (inside front cover).
$1~m=3.281~ft$, $1~mutchkin=0.42~L$, $1~m^{3}=10^{3}~L$
(a) Let V be the volume of a container ($a=1~ft)$.
$V=a^{3}=(1~ft)^{3}=(1~ft^{3})(\frac{1~m}{3.281~ft})^{3}=2.83\times10^{-2}~m^{3}$
$V=(2.83\times10^{-2}~m^{3})(\frac{10^{3}~L}{1~m^{3}})(\frac{1~mutchkin}{0.42~L})=67~mutchkin$
(b) $1~noggin=0.28~mutchkin$, $1~gal=3.785~L$, $1~mutchkin=0.42~L$
$1~noggin=(1~noggin)(\frac{0.28~mutchkin}{1~noggin})(\frac{0.42~L}{1~mutchkin})(\frac{1~gal}{3.785~L})=0.031~gal$
