Question

A conical tank has height 3 m and radius 2 m at the top. Water flows in at a rate of 1.6m3/min1.6m3/min. How fast is the water level rising when it is 1.11.1 m? (If you use decimal notation, give your answer to at least four decimal places.) The speed of the water level rising is =

Answer 1

Explanation:

Given that a conical tank has height 3 m and radius 2 m at the top. Water flows in at a rate of 1.6m^3/min

We know in a cone the ratio of radius to height is constant equal to tangent of semivertical angle.

i.e.
`(r)/(h) =K`

Hence we get radius when height was 1.11 m is

`(2)/(3) =(r1)/(1.1) \\r1 = 0.7333`

V' = 1.6

Volume of cone =
`(1)/(3) \pi r^2 h \\= (1)/(3) \pi (kh)^2 h\\=(1)/(3) \pi kh^3` where k = 2/3

`V' = \pi k h^2 h'\\1.6 = \pi (2)/(3) (1.1)^2 h'\\1.6 = 0.8067 \pi h'\\h'=(1.983)/(\pi)` m/sec.