Question

Casting of size 500mm$\times$400mm$\times$200mm solidifies in 30 min. The solidification time for a casting of size 500mm$\times$300mm$\times$100mm under similar conditions is

• A. 41.5 min
• B. 18.6 min
• C. 11.5 min
• D. 15.3 min

Answer 1

The correct option is C 11.5 min

Casting size${}_1$

$=500\times 400\times 200\to t_1=30min$

Casting size${}_2$

$=500\times 300\times 100\to t_2=?$

The solidification time, 't' is proportional

Thus, $t_2=t_1{\left(\frac{M_2}{M_1}\right)}^2=30[\left(\frac{500\times 300\times 100}{500\times 400\times 200}\right)\times \left(\frac{2\left[\right(500\times 400)+(400\times 200)+(500\times 200\left)\right]}{2\left[\right(500\times 300)+(300\times 100)+(500\times 100\left)\right]}\right)]t_2=11.5min$