ice and if the thickness is decreaing at a rate of 1/4 in/hr, how fast is the volume of the ice changing when the ice is 2 inches thick?
The surface of the ice is at a radius of 242 inches, so the outer hull of the ice hemisphere has surface area of 2*Pi*r^2 = 117128*Pi square inches. Therefore, the volume of the ice is changing at a rate of -117128*Pi cubic inches per inch that the radius decreases. Since the radius is decreasing at 1/4 inch per hour, the volume of the ice is changing at a rate of -29282*Pi cubic inches per hour, or roughly 91992 in^3/hr. (This is also 53.24 ft^3/hr.)
