Question

Ratio of solidification time of a cylindrical casting (height = radius) of that of a cubic casting of side two times the height of cylindrical casting is

• A. 0.5625

Answer 1

The correct option is A 0.5625

$T_{cy}=k{\left[\frac{V}{A}\right]}^2=k{\left[\frac{\pi r^2\times h}{2\pi r^2+2\pi rh}\right]}^2$

$\text{Given, h = r}$

$T_{cy}={\left[\frac{\pi r^3}{4\pi r^2}\right]}^2\Rightarrow T=k\left[\frac{r^2}{16}\right]$

$T_{cu}=k{\left[\frac{V}{A}\right]}^2=k{\left[\frac{a^3}{6a^2}\right]}^2$

$\text{But a = 2h = 2r}$

$T_{cu}=k\left[\frac{4r^2}{36}\right]$

$T_{cy}/T_{cu}=\left[k\left[\frac{r^2}{16}\right]\right]+\left[k\frac{r^2}{9}\right]=\frac{k{r}^2}{16}\times \frac{9}{k{r}^2}$

$=\frac{9}{16}=0.5625$