Flow rate of water = 10(m/min) = 1/6 (m/s)

Area of cross section of the pipe

= pie*radius^2 = pie*(2.5*10^(-3))^2

= 19.635*10^(-6) sq meter

Volume of cone = 1/3*pie*height*(Base radius)^2

= 0.********** cubic meter

The time taken in seconds for the cone to fill up would be the ratio of its volume to the flow rate of water.

Therefore (volume of cone/volumetric flow rate)

= 0.**********/19.635*10^(-6)= 512 seconds.