Question

A spherical scoop of vanilla ice cream with radius of 2 inches is dropped onto the surface of a dish of hot chocolate sauce. as it melts, the ice cream spreads out uniformly forming a cylindrical region 8 inches in radius. assuming the density of the ice cream remains constant, how many inches deep is the melted ice cream? express your answer as a common fraction.

Answer 1

The formula for the volume of a sphere is
V = (4/3)π·r³
so the scoop has a volume of
V = (4/3)π·(2 in)³ = 32π/3 in³

The formula for the volume of a cylinder is
V = π·r²·h
Since the cylinder has the same volume as the sphere, we have
32π/3 in³ = π·(8 in)²·h
h = (32π in³)/(3·64π in²) = 1/6 in