Answer:
34.16 cm
Step-by-step explanation:
side of square base = x
height = h
area, A = 3500 cm^2
Area = x² + 4xh = 3500
4 xh = 3500 - x²
h = (3500 - x²)/4x
Volume = Area of base x height
V = x² h
V = x² (3500 - x²)/4x
V = (3500 x - x³) / 4
Differentiate volume with respect to x
dV/dx = (3500 - 3x²) / 4
It is equal to zero for maxima and minima
3500 - 3x² = 0
x = 34.16 cm
Now differentiate again
d²V/dx² = 6x / 4
It is negative so the volume is maximum.
Thus, for x = 34.16 cm, the volume is maximum.
