Volume Expression

**gearshifter** · November 1st 2008, 11:04 AM

A water trough is $8$ m long and its cross-section is an isosceles trapezoid which is $150$ cm wide at the bottom and $250$ cm wide at the top, and the height is $50$ 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.

**Shyam** · November 1st 2008, 02:43 PM

Originally Posted by gearshifter

A water trough is $8$ m long and its cross-section is an isosceles trapezoid which is $150$ cm wide at the bottom and $250$ cm wide at the top, and the height is $50$ 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, $V= Area \times Length$

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

$V=(800d^2+120000d)\;\;cm^3$

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