Related Rates Question

Question

My circular swimming pool has a 30 foot diameter and is 6 feet tall. The flow rate from my spigot into the pool is about 1.84 feet per minute. How fast is the water level, h, rising at the moment when the water level is at a height of 4.2 feet?

 

I found that the water level is rising at a rate of 0.231 ft/min. Could somebody please confirm this?

Answer 1

Let V = volume of water at time t minutes

       h = depth of water at time t minutes

 

Given:  dV/dt = 1.84 ft³/min

Find:  dh/dt when h = 4.2 ft

 

V = πr²h = π(15)²h = 225πh

 

So, dV/dt = 225π(dh/dt)

 

       1.84 = 225π(dh/dt)

 

           dh/dt = 1.84/(225π) ≈ 0.0026 ft/min

 

Note:  dh/dt is constant for any value of h, 0 < h < 6.    

Answer 2

πr²h = 1.84 ft³ /min  - as long as flow rate is constant and independent of height of water in the pool.

 

3.14 x 15²ft² x h = 1.84  ft³ /min

calculate h

:)