Question

A solid cylinder of diameter D and height equal to D, and a solid cube of side L are being sand cast by using the same material. Assuming there is no superheat in both the cases, the ratio of solidification times of the cylinder to the solidification time of the cube is

• A. $(2L/D{)}^2$
• B. $(L/D{)}^2$
• C. $(2D/L{)}^2$
• D. $(D/L{)}^2$

Answer 1

The correct option is D $(D/L{)}^2$

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

$\text{For cube :}$

$V=L^3,A=6L^2$

$t_{cube}=k{\left(\frac{L}{6}\right)}^2$

$\text{For cylinder :}$

$V=\frac{\pi }{4}{D}^3$

$A=\frac{\pi D^2}{2}+\pi D^2=\frac{3\pi D^2}{2}$

$t_{\text{cylinder}}=k{\left(\frac{D}{6}\right)}^2$

$\text{Ratio of solidification time,}$

$\frac{t_{\text{cylinder}}}{t_{\text{cube}}}={\left(\frac{D}{L}\right)}^2$