SOLUTION: 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 d

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?
=====================
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.
.
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].
.
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.).
.
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.
.
Let's use our formula to put this all together:
V = (1/2)*(10)*(6.5)*(2640)
V = 85,800
.
There are 85,800 cubic feet in the channel.
.
Hope this helps!
.
Ms.Figgy
math.in.the.vortex

RELATED QUESTIONS
A park has a water channel with a semicircular cross section that has a diameter of 13ft. (answered by greenestamps,ikleyn)

A park has a water channel with a semicircular cross section that has a radius of 13ft.... (answered by ikleyn,Alan3354)

A survey of some residents of a certain community was conducted to determine the number... (answered by greenestamps)

A new cylindrical tank will be installed in a pre-existing rectangular channel measuring... (answered by Theo)

A survey shows that 63 % of the people watch a news channel whereas 76% watch another... (answered by jorel555)

A weather channel covers local weather six times per hour for a period of 2 minutes. If... (answered by Boreal)

A customer subscribes to a movie channel that costs $18.00 / month. How much will the... (answered by Fombitz)

An n-byte message is being sent. For greater reliability, k independent information... (answered by ikleyn)

Suppose a cylindrical storage tank is to contain V=16,000π cubic feet (about 400,000... (answered by josgarithmetic,josmiceli)