$($Q$1)$ a$.$ Consider a hot spherical ball and a cylinder of same diameter, both at the same initial temperature $(\backslash ($ T$\_\{$i$\}\backslash ))$ and made of the same material, immersed in a colder fluid at temperature $\backslash ($ T$\_\{$i$\}/10\backslash ).$ Which of these objects will earlier reach a temperature of $\backslash ($ T$\_\{$i$\}/5\backslash )?$ Consider the cylinder length same as its diameter and Bi$<mn>0</mn><mn>.</mn><mn>1</mn>$ for both. $($hint: you may explain your answer with proper reasoning without finding the exact expression for the cooling time.$)$