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A water trough is 6 m long and its cross-section is an isosceles triangle which is 60 cm wide at the top, and the height is 30 cm.

A water trough is 6 m long and its cross-section is an isosceles triangle which is 60 cm wide at the top, and the height is 30 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.
 
Answer should be in cm3. 

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Mark M. | Mathematics Teacher - NCLB Highly QualifiedMathematics Teacher - NCLB Highly Qualif...
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Draw and label a diagram.
 
At the depth "d" the cross section of the water is a similar triangle to the cross section of the trough.
The ratio of the corresponding sides is d/30. Therefore width of the water cross section is (d/30)(60), 20d.
The water cross section has an area of (1/2)(20d)d, 10d2cm2
The volume of water in the trough is (10d2cm2)(600cm), 6000d2cm3