Answer:
a) 13 mins
b) 18 mins
Explanation:
solidification time = 10 minutes
height-to-diameter ratio = 1
applying the expression for calculating solidification time
t = B [tex](\frac{V}{A} ) ^n[/tex] --------- ( 1 )
n = 1.5
B = ?
t = 10 minutes
V = [tex]\frac{\pi d^2}{4} H[/tex]
A = [tex]\frac{\pi d^2}{2} + \pi dH[/tex]
back to equation 1
making B subject of the formula ; B = [tex]\frac{147}{d^{1.5} }[/tex]
a) Determine the solidification time if the cylinder height is doubled
t = B [tex](\frac{V}{A} ) ^n[/tex]
substitute : B = [tex]\frac{147}{d^{1.5} }[/tex] , H = 2D , V = [tex]\frac{\pi d^2}{4} H[/tex] , A = [tex]\frac{\pi d^2}{2} + \pi dH[/tex] , n = 1.5
therefore ; t ( solidification time when height is doubled ) ≈ 13 mins
b) Determine the time if the diameter is doubled
t = B [tex](\frac{V}{A} ) ^n[/tex]
substitute ; B = [tex]\frac{147}{h^{1.5} }[/tex] , D = 2H , n = 1.5 , V = [tex]\frac{\pi d^2}{4} H[/tex], A = [tex]\frac{\pi d^2}{2} + \pi dH[/tex]
therefore ; t ( solidification time when diameter is doubled ) ≈ 18 mins
