The volume of the right-square prism may be expressed as
V = Ah,
where A is the cross-sectional area and h is the height. Since the cross-section is square, the area is
A = x2, where x is the side-length of the square. Hence, we may write the volume as
V = x2h.
The prism fits snugly through a square hole 10 inches on a side, so this implies x = 10 inches. We are also given that h = 4ft = 48inches, so
V = 102*48 = 4800 in3.
(Volume given in cubic inches.)
The volume of a right-circular cylinder with radius r and height H is
V = πr2H.
If the right-circular cylinder fits through the same hole as the prism, then r = 5. So we set the volume of the cylinder equal to the volume of the prism to find the height of the cylinder.
πr2H = 4800
π52H = 4800
25πH = 4800.
H = 4800/(25π) = 192/π, or
H ≅ 61.1 inches.
Hope that helps! Let me know if you need any clarification.