Question

A water tank has the shape of an inverted right circular cone with base radius 3 meters and height 6 meters. Water is being pumped into the tank at the rate of 12 meters3/sec. Find the rate, in meters/sec, at which the water level is rising when the water is 2 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).

Answer 1

let the radius of the water level be r m
let the height of the water be h m

make a sketch and by similarity:
h/r = 6/3
h/r = 2
h = 2r or r = h/2

V = (1/3)π r^2 h
= (1/3)π (h^2/4)(h) = (1/12)π h^3

dV/dt = (1/4) h^2 dh/dt
so when h= 2 and dV/dt = 12

12 = (1/4)((4)dh/dt
dh/dt = 12 m/sec

check my arithmetic, should have written it out on paper first.