Question

a rectangular swimming pool 10 m long and 5 m wide has a depth of 3 meters at one end and 1 meter at the other end. if water is pumped into the pool at the rate of 300 liters per min, at what rate is the water level rising when it is 1.5 m deep at the deep end?

Answer 1

To determine the rate at which the water level is rising, calculate the surface area of the trapezoidal pool at 1.5 meters depth and use the rate of water being pumped in to find the change in height over time.

Step-by-step explanation:

The question is asking for the rate at which the water level is rising in a trapezoidal swimming pool when the water is 1.5 meters deep at the deep end.

To solve this, we need to know the volume of water being added per minute and the surface area of the pool at the depth of 1.5 meters. Since the pool is trapezoidal, the surface area changes with depth.

With a water pump rate of 300 liters per minute (0.3 m3/min), we can set up a relationship between the rate of volume increase and the rate of height increase. Since the volume of the pool at any given depth is the surface area times the depth, we can write the formula as dV/dt = A(h) * dh/dt, where A(h) is the area as a function of the height h.

Assuming a linear change in width with respect to the pool's depth, we can calculate the width of the pool at 1.5 meters depth, then find the area at that depth, and finally calculate the rate of the water level rise (dh/dt) when the pool is 1.5 meters deep using the equation 0.3 m3/min = A(h) * dh/dt.