Let a = side of the base, b = base area, h = altitude
Let us assume it is a regular pyramid. The (altitude) height "h"
of apex from base square, slanting height and the side "a"
of the base square rise uniformly and proportionally when we move from the apex point to the base.
If height (altitude) h becomes x times, then side "a" of the base square becomes x times, the slanting height also becomes x times. Thus the area b
of the base square rises x² times.
Δh / h = Δa / a => Δb / b = 2 Δa / a = 2 Δh / h or h1/h2 = a1/a2
V = 1/3 b h = 1/3 a² h
d V / dt = 1/3 a² dh/dt + 1/3 h 2 a da/dt = 1/3 a² dh /dt + 2/3 h a (a/h) (dh/dt)
= 1/3 a² dh / dt + 2/3 a² dh/dt
dV/dt = a² dh/dt => dh/dt = (1/a²) dV/dt
h_0 = 8 cm a_0 = 6 cm at the base
When h = 6cm, h / h_0 = a/a_0 => a = a_0 * h / h_0 = 6*6/8 = 4.5 cm
dh/dt = 1/4.5² * 25 = 100/81 cm/sec = 1.23456790 cm/sec