A water filter has the shape of an inverted right circular cone with base radius 3 meters and height 9 meters. water is being pu
mped into the filter at the rate of 10 meters3/sec. find the rate, in meters/sec, at which the water level is rising when the water is 3 meters deep. give 2 decimal places for your answer. type your answer in the space below. if your answer is a number less than 1, place a leading "0" before the decimal point (ex: 0.35).
The volume of a cone is V = (1/3)πr³ We are given with radius and the height of cone, so we can solve for the radius as function of water level using ratio and proportion 3/9 = r/h r = h/3 Substituting V = πh³/81 Taking the derivative dV/dt = πh²/27 dh/dt Solving for dh/dt given dV/dt = 10 m³/s and h = 3 m dh/dt = 9.55 m/s
Hello there. <span> A water filter has the shape of an inverted right circular cone with base radius 3 meters and height 9 meters. water is being pumped into the filter at the rate of 10 meters3/sec. find the rate, in meters/sec, at which the water level is rising when the water is 3 meters deep. give 2 decimal places for your answer. </span> 9.55 m/s
