The radius of a right circular cylinder increases at a constant rate. Its altitude is a linear function of the radius and increases three times as fast as radius. When the radius is $1 \mathrm{cm}$ the altitude is $6 \mathrm{cm}$. When the radius is $6 \mathrm{cm}$, the volume is increasing at the rate of $1{ \mathrm{cm}}^3/\mathrm{s}$. When the radius is $36 \mathrm{cm}$, the volume is increasing at a rate of $n{ \mathrm{cm}}^3/\mathrm{s}$. The value of '$n$' is equal to