The trough shown in the figure has a triangular ends which lie in parallel planes. The top of the trough is a horizontal rectangle in 20 in. by 33 in., and the depth of the trough is 16 in.
(a.) How many gallons of water will it hold?
(b.) How many gallons does it contain when the depth of the water is 10 in.?
(c.) What is the depth of the water when the trough contains 3 gal.?
(d.) Find the wetted surface when the depth of the water is 9 in. (1 gal = 231 cu. in.)

Question

The trough shown in the figure has a triangular ends which lie in parallel planes. The top of the trough is a horizontal rectangle in 20 in. by 33 in., and the depth of the trough is 16 in. 
(a.) How many gallons of water will it hold?
(b.) How many gallons does it contain when the depth of the water is 10 in.?
(c.) What is the depth of the water when the trough contains 3 gal.?
(d.) Find the wetted surface when the depth of the water is 9 in. (1 gal = 231 cu. in.)

anonymous · Answer

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mathstudent55 · Answer

The volume of a prism is the area of the base multiplied by the length, L. Here the base of the prism is a triangle with a 20" base, b, and 16" height, h. The length of the prism is 33 in.
(a) V = (1/2)bhL = (1/2)(20)(16)(33) = 5280 cu in.
     V = (5280 cu in.) (1 gal)/(231 cu in.) = 22.9 gal