Answer:
a) See Below
b) See Below
c) See Below
Step-by-step explanation:
The relative solidification time is given by formula ![t_s=C_m(\frac{V}{A})^2](https://tex.z-dn.net/?f=t_s%3DC_m%28%5Cfrac%7BV%7D%7BA%7D%29%5E2)
Where C_m is the Chvorinov's constant given as 3.5
V is Volume
A is Surface Area
a)
<u>Sphere:</u>
Volume = ![\frac{4}{3}\pi r^3=\frac{4}{3}\pi (5)^3 = 523.6](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B3%7D%5Cpi%20r%5E3%3D%5Cfrac%7B4%7D%7B3%7D%5Cpi%20%285%29%5E3%20%3D%20523.6)
Surface Area = ![4\pi r^2=4\pi (5)^2 = 314.16](https://tex.z-dn.net/?f=4%5Cpi%20r%5E2%3D4%5Cpi%20%285%29%5E2%20%3D%20314.16)
Now putting in the formula:
Relative Solidification Time of Sphere =
minutes
Relatively, We can say t_s = 2.778 * C_m
<u>Cube:</u>
Volume = 10^3 = 1000
Surface Area = 6x^2 = 6(10)^2 = 600
Relative Solidification Time of Cube =
minutes
Relatively, We can say t_s = 2.778 * C_m
<u>Cylinder:</u>
Volume = ![\pi r^2 h = \pi (5)^2 (10)=785.4](https://tex.z-dn.net/?f=%5Cpi%20r%5E2%20h%20%3D%20%5Cpi%20%285%29%5E2%20%2810%29%3D785.4)
Surface Area = ![2\pi r^2 + 2\pi r h=471.24](https://tex.z-dn.net/?f=2%5Cpi%20r%5E2%20%2B%202%5Cpi%20r%20h%3D471.24)
Relative Solidification Time of Cylinder = ![t_s=C_m(\frac{V}{A})^2\\t_s=3.5(\frac{785.4}{471.24})^2\\t_s=9.72](https://tex.z-dn.net/?f=t_s%3DC_m%28%5Cfrac%7BV%7D%7BA%7D%29%5E2%5C%5Ct_s%3D3.5%28%5Cfrac%7B785.4%7D%7B471.24%7D%29%5E2%5C%5Ct_s%3D9.72)
Relatively, We can say t_s = 2.778 * C_m
b)
All of them have same relative solidification time. So we can say that all 3 of them are good for making risers.
c)
Since, we had
Relatively, We can say t_s = 2.778 * C_m
we get:
t_s = 2.778 * C_m = 2.778 * 3.5 = 9.72 minutes