Question

If the largest cube that can be carved out from a gold sphere has a thermal capacity of 'K' units, what would be the thermal capacity of the sphere?

Answer 1

Same material
$C_{cube}=C_{sphere}\frac{l_c}{r_s}=?$
$m_{cube}\times s_{cube}=m_{sphere}\times s_{sphere}$
$V_{cube}\times d_{cube}\times s_{cube}=V_{sphere}\times d_{sphere}\times s_{sphere}$
$(\therefore d_{cube}=d_{sphere},s_{cube}=s_{sphere})$
$V_{cube}=V_{sphere}$
$\Rightarrow l_c^3=\frac{4}{3}\pi r_s^3\Rightarrow \frac{l_c^3}{r_s^3}=\frac{4}{3}\pi$
$\Rightarrow \frac{l_c}{r_s}={\left[\frac{4\pi }{3}\right]}^{1/3}$