In sand-mold casting of a metal, it takes 180 seconds for complete solidification of a 27 cm^{3} cube-shaped casting. All other parameters remaining constant, the total solidification time (in seconds, rounded off to one decimal place) for a cylinder-shaped [radius = 1 cm and height = 6 cm] casting of the same metal, is _______.

# GATE MT 2019 Q43

Share

Solidification time t = k (V/A)2 From the given data tcube = 180 sec where V = 27 cm3 so a = 3cm Putting the formula we get 180 = k (27/54)2 In case of cylinder having r = 1 cm and h = 6 cm Putting the formula hwe get t = k (rh/2h+2r)2 Where volume = Πr2 h and area = 2Πr2 + 2 Πrh Hence tcylinder = kRead more

Solidification time t = k (V/A)

^{2}From the given data t

_{cube }= 180 sec where V = 27 cm^{3 }so a = 3cmPutting the formula we get

180 = k (27/54)

^{2}In case of cylinder having r = 1 cm and h = 6 cm

Putting the formula hwe get t = k (rh/2h+2r)

^{2}Where volume = Πr

^{2 }h and area = 2Πr^{2 }+ 2 ΠrhHence t

_{cylinder = }k (6/14)^{2}Comparing solidification time equation of cube and cylinder we got solidification time of cylinder

t = 180* (6/7)

See less^{2 }= 132.24 secVideo solution at 10:25. According to Choroniv rule, the time of solidification is related to square of length of casting. length is calculated by dividing volume by total area.

Video solution at 10:25.

According to Choroniv rule, the time of solidification is related to square of length of casting.

length is calculated by dividing volume by total area.

See less

See lessCorrect answer is in the range of 130-134. @Digbijaya igit described it best. Thank you. Some peripheral lines related to this topic: Solidification time, t= K (V/A)2

Correct answer is in the range of 130-134. digbijaya igit igit described it best. Thank you.

Some peripheral lines related to this topic:^{2}