A water trough is 8 feet long, and its cross section is an equilateral triangle with sides 2 feet long. Water is pumped into the trough at a rate of 7 cubic feet per second. How fast is the water level rising when the depth of the water is 1/2 foot?( Hint: First, what is the height h of an equilateral triangle of side length s? Next, what is the area of an equilateral triangle in terms of the side length s? Then write the area in terms of h. The volume of the water in the trough at time t is the product of the cross-sectional area with water and the length of the trough. )a) What is the height h of an equilateral triangle of side length s?h =    ? in ft  b) The water level is rising at a rate of    ? in ft/sec

Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter59: Areas Of Rectangles, Parallelograms, And Trapezoids
Section: Chapter Questions
Problem 79A
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A water trough is 8 feet long, and its cross section is an equilateral triangle with sides 2 feet long. Water is pumped into the trough at a rate of 7 cubic feet per second. How fast is the water level rising when the depth of the water is 1/2 foot?

Hint: First, what is the height h of an equilateral triangle of side length s? Next, what is the area of an equilateral triangle in terms of the side length s? Then write the area in terms of h. The volume of the water in the trough at time t is the product of the cross-sectional area with water and the length of the trough. )

a) What is the height h of an equilateral triangle of side length s?
h =    ? in ft  

b) The water level is rising at a rate of    ? in ft/sec  

 
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