Let a = side of the base, b = base area, h = altitude

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Detailed explanation:

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