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Question

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 (see figure below). Water is being pumped into the pool at 1/8 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?

_______m/min

Answer 1

Area of trapezoid = ( a + b ) h / 2

= ( 3 + 1 ) 12 / 2

= 24 m²

V _pool = A t ( h )

= 24 ( 6 ) = 144 m ³

x / y = 2 / 12. y = 6 x

V _water = ( x y ) / 2 _* 6 x = 1

V _w = 3 x y = 3 ( 1 ) ( 6 )

= 18 m³

a. V_{p /} V_w = 18 / 144 = 1 / 8 = .125 or 12.5 %

b. V = 3 x ( 6 x )

= 18 x ²

d V / d t = 18 ( 2 x d x / d t )

= 36 x d x / d t

1 / 8 = 36 ( 1 ) d x / d t

d x / d t = 1 / 288 m / min