Question

Two castings of the same material have same surface area. One casting is in the form of a sphere and other is a cube. The ratio of solidification time for the sphere to that for the cube is ________ .

• A. 1.65
• B. 1.909
• C. 1.101
• D. 0

Answer 1

The correct option is B 1.909


$A_1=A_{2}4\pi r^2=6a^2\frac{r}{a}={\left(\frac{3}{2\pi }\right)}^{1/2}\frac{t_1}{t_2}={\left(\frac{v_1}{v_2}\right)}^2={\left(\frac{4}{3}\frac{\pi r^3}{a^3}\right)}^2={\left(\frac{4}{3}\pi \right)}^2{\left(\frac{3}{2\pi }\right)}^3=\frac{6}{\pi }=1.909$