Determine the height of the marble column if its volume is 2400 cubic dm.

Determine the height of the marble column if its volume is 2400 cubic dm. The marble column has a square at the base with a perimeter of 200 cm.

Problem data: V (volume of a given marble column) = 2400 dm3 (in SI V = 2.4 m3); the base of the column is a square; P (perimeter of the square) = 200 cm (SI P = 2 m).

To determine the height of a given marble column, use the formula: V = S * h = a ^ 2 * h = (0.25P) ^ 2 * h, whence h = V / (0.25P) ^ 2.

Let’s make a calculation: h = 2.4 / (0.25 * 2) ^ 2 = 9.6 m.

Answer: The height of a given marble column is 9.6 m.