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

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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.

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 lessSolidification 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 sec

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}