A) 1 : 1
B) \[\frac{4\pi }{3}\,\,:\,\,1\]
C) \[{{\left( \frac{\pi }{6} \right)}^{1/3}}:\,\,1\]
D) \[\frac{1}{2}\,{{\left( \frac{4\pi }{3} \right)}^{2/3}}:\,\,1\]
Correct Answer: C
Solution :
Q = s A t (T4 ? T04) If T, T0, s and t are same for both bodies then \[\frac{{{Q}_{sphere}}}{{{Q}_{cube}}}=\frac{{{A}_{sphere}}}{{{A}_{cube}}}=\frac{4\pi {{r}^{2}}}{6{{a}^{2}}}\] ?..(i) But according to problem, volume of sphere = Volume of cube Þ \[\frac{4}{3}\pi {{r}^{3}}={{a}^{3}}\] Þ \[a={{\left( \frac{4}{3}\pi \right)}^{1/3}}r\] Substituting the value of a in equation (i) we get \[\frac{{{Q}_{sphere}}}{{{Q}_{cube}}}=\frac{4\pi {{r}^{2}}}{6{{a}^{2}}}=\frac{4\pi {{r}^{2}}}{6{{\left\{ {{\left( \frac{4}{3}\pi \right)}^{1/3}}r \right\}}^{2}}}\] \[=\frac{4\pi {{r}^{2}}}{6\,{{\left( \frac{4}{3}\pi \right)}^{2/3}}{{r}^{2}}}={{\left( \frac{\pi }{6} \right)}^{1/3}}:1\]
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