Hi guys can you help me! Please teach me step by step.. I really need it. pls! Thank you.........

A swimming pool is 12 meters long, 6 meters wide, 1 meter deep at the shallow end, and 3 meters deep at the deep end. Water is being pumped into the pool at ¼ cubic meter per minute, and there is 1 meter of water at the deep end.

a.) What percent of the pool is filled?
b.) At what rate is the water level rising?

2 answers

The cross-section is a trapezoid of area

(1+3)/2 * 6 = 12 m^2
So, the volume is 12 * 12 = 144 m^3

with only 1 m of water, the cross-section of the water is a triangle of area 3/2 m^2, so its volume of water is 18 m^3

Thus the pool is 18/144 = 1/8 full

At depth y of water, the surface has width y/2, so

v = (1/2)(y)(y/2)(12) = 3y^2

dv/dt = 6y dy/dt
At y=1, then

1/4 = 6 dy/dt
and the height is rising at 1/24 m/s

As usual, check my arithmetic.
Nope not a thing