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A trough is $ 10 ft $ long and its ends have the shape of isosceles triangles that are $ 3 ft $ across at the top and have a height of $ 1 ft. $ If the trough is being filled with water at a rate of $ 12 ft^3/ min, $ how fast is the water level rising when the water is $ 6 inches $ deep?

02:22

Wen Z.

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 9

Related Rates

Derivatives

Differentiation

Campbell University

Oregon State University

Harvey Mudd College

Lectures

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We're trying to figure out how fast the water level is rising, so we know that B is three H because three over one is B over H. Therefore we know V is be times Age, so three h times age. Remember, be a screech. Times 10 divide by two Go for V is 15 h squared 30 over 2 15 Therefore, Devi over DT is 30 h times d h over DT, which means that 12 is 30 times 0.5 times d h over DT, which means that the age over D she is for over 50.8 feet per minute.

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