Water is dropped at the rate of 2 m3/s into a cone of semi-vertical angle 45°. If the rate at which periphery of water surface changes when the height of the water in the cone is 2 m is d, then the value of 5d is _______

We have         dVdt=2  or  ddt13πr3=2      Here,   r=h   as   θ=45°or     πr2drdt=2     or   drdt=2πr2                                                1Now,   perimeter  =2πr=p   let∴   ddt2πr=2π2πr2=4r2   Using  equation  1      2When  h=2m,  r=2mHence,  dpdt=44=1  m/s.