A) both of them will cool down at the same rate
B) the cube will cool down faster than the sphere
C) the sphere will cool down faster than the cube
D) whichever of the two is heavier will cool down faster
Correct Answer: B
Solution :
Area of sphere = area of cube \[4\pi {{r}^{2}}=6{{\alpha }^{2}}\] \[r=a\sqrt{\frac{3}{2\pi }}\] Volume of sphere \[=\frac{4}{3}\pi {{r}^{3}}\] \[={{a}^{3}}\frac{4}{3}\pi {{\left\{ \sqrt{\frac{3}{2}\pi } \right\}}^{3}}={{a}^{3}}\sqrt{\frac{6}{\pi }}\] But volume of cube \[={{a}^{3}}\] Volume of sphere > volume of cube Volume of cube is less, so cube will cool rapidly.
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