Question

In the sand casting process, a sphere and a cylinder of equal volumes are separately cast from the sand molten metal under identical conditions. The height and diameter of the cylinder are equal. The ratio of the solidification time of the sphere to that of the cylinder is

• A. $1.14$
• B. $1.31$
• C. $0.76$
• D. $0.87$

Answer 1

The correct option is B $1.31$

$\text{Given data:}$

$\text{Let}{D}_s:\text{diameter of sphere}$

$D_c:\text{diameter of cylinder}$

$\frac{\pi }{4}{D}_c^3=\frac{\pi }{6}{D}_s^3$

$D_s^3=\left(\frac{3}{2}{D}_c^3\right)$

$D_s=1.144D_c$

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

$\Rightarrow \frac{T_s}{T_c}={(\frac{V_s}{A_s}\times \frac{A_c}{V_c})}^2$

$={(\frac{D_s}{6}\times \frac{6}{D_c})}^2={\left(\frac{1.144D_c}{D_c}\right)}^2$

$\frac{T_s}{T_c}=1.31$