Question

The solidification time of 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 the same material and size are case using a 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

• A. $\frac{36}{25}$
  
• B. 1
• C. $\frac{25}{36}$
  
• D. $\frac{6}{5}$
  

Answer 1

The correct option is A $\frac{36}{25}$

$T_{\text{solidification}}=k{\left(\frac{V}{A}\right)}^2$

$\Rightarrow \frac{T_1}{T_2}=\frac{k{\left(\frac{V_1}{A_1}\right)}^2}{k\left(\frac{V_2}{A_2}\right)}$

$V_1=V_2$

$\Rightarrow \frac{T_1}{T_2}=\frac{A_2^2}{A_1^2}=\frac{{\left(6a^2\right)}^2}{{\left(5a^2\right)}^2}=\frac{36}{25}$