Answer in the back of the book is wrong?

[Jamin2112]

I'm tutoring a kid in high school Calculus and his book gives an answer of (25√3)/4 for the following question.

A trough of length 6m has a uniform cross-section which is an equilateral triangle with sides of length 1. Water leaks from the bottom of the trough at a constant rate of 0.1 m³/min. Find the rate at which the water level is falling at the instant when the water is 20cm deep.

 

[Ray Vickson]

I'm tutoring a kid in high school Calculus and his book gives an answer of (25√3)/4 for the following question.

A trough of length 6m has a uniform cross-section which is an equilateral triangle with sides of length 1. Water leaks from the bottom of the trough at a constant rate of 0.1 m³/min. Find the rate at which the water level is falling at the instant when the water is 20cm deep.

What is YOUR answer? Why do you think the book'a answer is wrong?

 

[Jamin2112]

What is YOUR answer? Why do you think the book'a answer is wrong?

The area of an equilateral triangle is A=h²/sqrt(3) if h is the height when it is standing on one of its tips
---->
The volume of the trough in question is defined by the equation V=6*A=6*h²/sqrt(3)
---->
dV = (12/sqrt(3))*h*dh by differentiation
---->
dh = dv*(sqrt(3)/12)*(1/dh)
--->
dh = sqrt(3)/24 when dv=0.1 and h=0.2.

Is this shoddy arithmetic by me, or am I a failure of a tutor, or both?

 

[Ray Vickson]

The area of an equilateral triangle is A=h²/sqrt(3) if h is the height when it is standing on one of its tips
---->
The volume of the trough in question is defined by the equation V=6*A=6*h²/sqrt(3)
---->
dV = (12/sqrt(3))*h*dh by differentiation
---->
dh = dv*(sqrt(3)/12)*(1/dh)
--->
dh = sqrt(3)/24 when dv=0.1 and h=0.2.

Is this shoddy arithmetic by me, or am I a failure of a tutor, or both?

I agree with your answer.

 

[Joffan]

I'm getting the same as you for m/min (except that dh/dt is negative). Are those the units requested?

100 litres per minute is quite the leak.