SOLUTION: A swimming pool 50m long and 25m wide is 5.5m deep at one end and 1.5m deep at the other.The floor of the pool slopes uniformly. find the volume of the water when it is filled..

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Question 1124873: A swimming pool 50m long and 25m wide is 5.5m deep at one end and 1.5m deep at the other.The floor of the pool slopes uniformly. find the volume of the water when it is filled..
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


View the pool as a trapezoidal prism.

The base of the prism is a trapezoid; the height of the trapezoid is the length of the pool (50m); the bases of the trapezoid are the depths at the two ends (1.5m and 5.5m).

The height of the prism is the width of the pool (25m).

The volume of the prism is (area of the trapezoidal base) times (height):

The area of the trapezoidal base is (height = 50) times (average of the bases = (1.5+5.5)/2 = 3.5)

Area of trapezoidal base: 50m * 3.5m = 175m^2

Volume of pool: 175m^2 * 25m = 4375m^3