# GATE Papers >> Mechanical >> 2015 >> Question No 46

Question No. 46

The solidification time of a casting is proportional to ${\left(\frac{V}{A}\right)}^{2}$ ,Where V is the volume of the casting and A is the total casting surface area losing heat. Two cubes of same material and size are cast using sand casting process. The top face of one of the cubes is completely insulated. The ratio of the solidification time for the cube with top face insulated to that of the other cube is

##### Answer : (B) $\frac{36}{25}$

Solution of Question No 46 of GATE 2015 Mechanical Paper
Solidification time ( ts ) = K$/cdot$ $\left(\frac VA\right)^2$

K = solidifiaction factor

V = vol. of casting

A = surface area of casting

$ts\;\alpha\;\left(\frac VA\right)^2$

Suppose ,vol. of cube = x = $V_1=V_2$

area of plane = y

$\therefore A_1=5\cdot Y\;\&\;A_2=6\cdot Y$

$ts_1\propto(x^2/25\cdot y^2)\;\;\;\;\;\;ts_2\propto(x^2/36\cdot y^2)$

$\therefore$  $\frac{ts_1}{ts_2}=\frac{36}{25}$ .