Volume of regular cylinder #V# = #pir^2h#,
Differentiating implicitly with respect to #t# [ time] using the product rule.
#d[uv]=vdu+udv#, where #u# and #v# are each functions of some other variable, in this example #t# [where #u=r^2# and #v=h]#
So #d/dt[V]#= #pi[hd/dt[r^2]+r^2d/dt[h]]#=#pi[2rhdr/dt+r^2dh/dt]#......#[1]#
We know #[dV]/dt=5#, from the question, we also know that the height #h# is constant at # 1 cm # [10mm] and #[dh]/dt# must equal zero , [since there is no change in height with respect to time.]
So ......#[1]# can expressed, #5=pi[2r[dr]/dt+0]# which yields,
#[dr]/dt = 5/[2pir#, i.e the rate of change of the radius with respect to time, from which the answers given above are obtained.