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Math Help - Volume Expression

  1. #1
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    Volume Expression

    A water trough is m long and its cross-section is an isosceles trapezoid which is cm wide at the bottom and cm wide at the top, and the height is cm. The trough is not full. Give an expression for V, the volume of water in the trough in cm3, when the depth of the water is d cm.
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  2. #2
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    Quote Originally Posted by gearshifter View Post
    A water trough is m long and its cross-section is an isosceles trapezoid which is cm wide at the bottom and cm wide at the top, and the height is cm. The trough is not full. Give an expression for V, the volume of water in the trough in cm3, when the depth of the water is d cm.
    Please see attached diagram,

    Area of cross-section = \frac{1}{2}(EH +AB)AF

    = \frac{1}{2}(150+2d +150)d

    = \frac{1}{2}(300d+2d^2)

    = (d^2+150d)\;\;cm^2

    Volume, V= Area \times Length

    V=(d^2+150d)(800)

    V=(800d^2+120000d)\;\;cm^3
    Attached Thumbnails Attached Thumbnails Volume Expression-graph16.jpg  
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