Question 461941: You are monitoring a V-shaped channel that carries water runoff from a section highway. the channel is 8feet deep, 10 feet across, and 1/2 mile long. when the the water is 61/2 deep, about how many cubic feet of water will ther be in the channel?
Answer by math-vortex(648)   (Show Source):
You can put this solution on YOUR website! you are monitorina a V-shaped channel that carries water runoff from a section highway. the channel is 8feet deep, 10 feet across, and 1/2 mile long. when the the water is 61/2 deep, about how many cubic feet of water will ther be in the channel?
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The shape of the channel is a triangular prism. (the underwater v-shape sides, and a line drawn from side to side on the surface form an inverted triangle. The distance of the channel adds the other dimension.
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We need to use the formula for the volume of this shape to find the amount of water contained in it. The formula for the volume of a triangular prism is
V = [the area of the triangle] x [the length of the channel].
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The formula for the area of a triangle is
A = [1/2] x [base] x [height].
In your problem, the base of the triangle is the distance across the channel (10 ft.), and height of the triangle is the depth of the channel (8 ft.).
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The channel is 1/2 mile long. We need to convert this to feet. There are 5,280 feet in one mile, so there are 2,640 feet in a half-mile.
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Let's use our formula to put this all together:
V = (1/2)*(10)*(6.5)*(2640)
V = 85,800
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There are 85,800 cubic feet in the channel.
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Hope this helps!
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Ms.Figgy
math.in.the.vortex
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