A sphere of radius \( 5 \) mm is initially in equilibrium at \( 400^{\circ}\text{C} \) inside a furnace. It is suddenly taken out and dropped into a well stirred water bath held at \( 20^{\circ}\text{C} \), with a convection heat transfer coefficient of \( 500 \) W/(m2K). Over this range of temperatures the sphere material has density \( \rho = 3000 \) kg/m3, thermal conductivity \( k = 10 \) W/(mK), and specific heat \( c = 1000 \) J/(kgK). Neglecting radiation, find the time needed for the centre of the sphere to cool from \( 400^{\circ}\text{C} \) to \( 50^{\circ}\text{C} \). Give the answer in seconds, rounded off to 2 decimal places.