Yefim S. answered • 6d

Math Tutor with Experience

Volume V of water we evaluate as volume of cone: V = 1/3 πr^{2}h, where r is radius of base of cone, h is hite.

WE have from similyarity: r/h = 4/16, from here h = 4r or r = h/4, then V = 1/3π(h/4)^{2}·h = 1/48πh^{3},

V' = 1/48π·3h^{2}·h'; V' = 1/16πh^{2}·h'; h' = 16V'/(πh^{2});

h' = (16·2 cm^{3}/min)/(π·8^{2}cm^{2}) = 1/(2π) cm/min;

rate of grow depth h' = 1/(2π) cm/min