Answer :
Answer:
a) See Below
b) See Below
c) See Below
Step-by-step explanation:
The relative solidification time is given by formula [tex]t_s=C_m(\frac{V}{A})^2[/tex]
Where C_m is the Chvorinov's constant given as 3.5
V is Volume
A is Surface Area
a)
Sphere:
Volume = [tex]\frac{4}{3}\pi r^3=\frac{4}{3}\pi (5)^3 = 523.6[/tex]
Surface Area = [tex]4\pi r^2=4\pi (5)^2 = 314.16[/tex]
Now putting in the formula:
Relative Solidification Time of Sphere = [tex]t_s=C_m(\frac{V}{A})^2\\t_s=3.5(\frac{523.6}{314.16})^2\\t_s=9.72[/tex] minutes
Relatively, We can say t_s = 2.778 * C_m
Cube:
Volume = 10^3 = 1000
Surface Area = 6x^2 = 6(10)^2 = 600
Relative Solidification Time of Cube = [tex]t_s=C_m(\frac{V}{A})^2\\t_s=3.5(\frac{1000}{600})^2\\t_s=9.72[/tex] minutes
Relatively, We can say t_s = 2.778 * C_m
Cylinder:
Volume = [tex]\pi r^2 h = \pi (5)^2 (10)=785.4[/tex]
Surface Area = [tex]2\pi r^2 + 2\pi r h=471.24[/tex]
Relative Solidification Time of Cylinder = [tex]t_s=C_m(\frac{V}{A})^2\\t_s=3.5(\frac{785.4}{471.24})^2\\t_s=9.72[/tex]
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