Topic: Manufacturing Processes
Two castings of the same metal have the same surface area. One casting is in the form of a sphere and the other is a cube. What is the ratio of the solidification time for the sphere to that of the cube?
- A. 3/4
- B. 6/pi
- C. 3pi/8
- D. 5/4pi
Answer: B. 6/pi
Explanation: According to Chvorinov's rule, solidification time t = k * (V/A)^2. For a cube with side 'a', the volume is a³ and surface area is 6a^2, giving t_cube = k * (a² / 36). For a sphere with radius 'r', the volume is (4/3)*pi*r³ and surface area is 4*pi*r², giving t_sphere = k * (r² / 9). Setting the surface areas equal (6a^2 = 4*pi*r²) implies a² / r² = 4*pi / 6. The ratio t_sphere / t_cube evaluates to (r² / 9) / (a² / 36) = 4 * (r² / a²) = 4 * (6 / 4*pi) = 6 / pi.