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

1/6in

Step-by-step explanation:

In order to find the height of the melted ice-cream, first we need to find volue of a sphere then a cylinder and equate them.

As we know, the volume of a sphere is defined as:

V = (4/3) π·r³

therefore, scoop has:

V = (4/3) π· (2 in) ³ = > 32π/3 in³

Next is to find the volume of a cylinder

V = π·r²·h=> π· (8 in) ²·h

Since the cylinder has the same volume as the sphere, we have

32π/3 in³ = π· (8 in) ²·h (simplifying the equation)

We have, h = (32π in³) / (3x64π in²) = 1/6 in

Answer: h=1/6in